'Bucking' as opposing
The phrases "buck traffic" and "buck a trend" are examples of the verb buck used in the sense 1(b) below (from Merriam-Webster's Eleventh Collegiate Dictionary):
buck vt (1750) 1 a archaic : BUTT [meaning "to to strike or shove with the head or horns"] b : OPPOSE, RESIST {bucking the system} 2 : to throw (as a rider) by bucking 3 : to charge into (as a headwind) 4 a : to pass esp. from one person to another b : to move or load (as heavy objects) esp. with mechanical equipment
The Random House Historical Dictionary of American Slang (1993) has this entry for buck in the relevant sense:
buck v. 1. to defy; resist; challenge successfully. usu. trans[itive] or constr[ued] with against. Now S[tandard] E[nglish]. [First cited examples:] 1846 in Utah Hist[orical] Q[uarter]ly V (1932) 36: The Mormons would buck against it. 1878 in Seal and Salmon Fisheries IV 6: I have taken the names of all Indians that have bucked against my authority.
The word also appears in J.S. Farmer & W.E. Henley, Slang & Its Analogues (1890):
BUCK. ... Verb (American) — 1. To oppose; to run counter to. {Possibly a corruption of butt, or from BUCK as applied to a horse.}
'Bucking traffic' as 'recklessly going the wrong way'
The earliest matches for "bucking traffic" are from the first quarter of the twentieth century. The earliest sense of "buck traffic" seems to have been "to go against posted traffic right-of-ways. From the [Philadelphia, Pennsylvania] Public Ledger (November 11, 1919):
BUCKS TRAFFIC, NOW HELD
Navy Sailor Accused of Stealing Automobile in West Chester
Failure to obey a traffic signal at Broad and Walnut streets last night caused the arrest of John Sims, a negro sailor, for stealing the automobile he was driving.
...
Going south on Broad street, he failed to observe that the traffic semaphore was set against him, drove past it and was halted by Reserve Patrolman Stever. Stever's questioning brought out the fact, according to the police, that the car was a stolen one, and Sims was arrested.
From the [Philadelphia, Pennsylvania] Evening Public Ledger (January 21, 1921):
SAILORS IN CRASH, DRUNK, IS CHARGE
Two Service Men and Chauffeur Held After Machine Hits Trolley Car
TRIED TO "BUCK TRAFFIC"
Two sailors and a civilian, much the worse for violation of the prohibition amendment, according to the police, were injured last night at Eleventh and Winter streets when their motor car crashed into a trolley.
...
They were seen driving south in Eleventh street by Thomas Paxton, a motorman of an Eleventh street car, the machine careening madly from side to side and "bucking the traffic," as it runs north on that street.
Fearing an accident, Paxton stopped his car about thirty feet from Vine street and thought the drivers of the automobile would certainly see it and avoid a collision. But not so; the party was not bothering to look at little things like trolleys; they struck it head on.
From "Father M'Dermott Is Hurt by Trolley at 4th and Market," in the [Philadelphia, Pennsylvania] Evening Public Ledger (February 24, 1922):
Father McDermott, who is in his seventies, was in another street accident last August. He was hit by an automobile at Fourth and Walnut streets and was hurt slightly. He refused to prosecute the driver of the car, who had been "bucking" traffic, because the man's children burst into tears after the accident.
From "Problems to Solve," in the Washington [D.C.] Herald (November 7, 1922):
Here are a number of conditions which it may be possible to deal with to the great benefit of the city:
"First. The tendency on the part of nearly all truck drivers and many pleasure automobile drivers to ignore the rule, in the absence of traffic direction, that the car to the right at a crossing has the right of way.
"Second. The tendency on the part of drivers of many wagons and trucks to 'buck' traffic by driving the wrong way on one-way streets.
From "P.R.T. Turnback Called Nuisance," in the [Philadelphia, Pennsylvania] Evening Public Ledger (November 29, 1922):
Many of the business men say trouble on the elevated started with the opening of the Frankford L, when the P. R. T. diverted the Frankford L trains to the Market Street L lines. The added traffic, they say, caused congestion and delays. Others say that the Sixty-third street turnback switch is responsible and that it would be a wiser policy to run all trains through to Sixty-ninth street and around the loop instead of bucking traffic at the crossover at Sixty-third street.
From Philadelphia Traffic Survey: Report – Issues 1–7 (1929) [combined snippets]:
On two-way streets, a large percentage of motor vehicle accidents are head-on collisions, most of the streets of this type being too narrow to accommodate more than two lanes of traffic each way, with the result that the driver who is in a hurry will take a chance by turning into the opposite travel lane when passing a vehicle going in the same direction that is compelled to keep to the center lane due to vehicles parked along the curb. Woodland, Chester, Baltimore, Ridge, Germantown, and Frankford Avenues are examples of this type. All of them have contributed a large number of head-on collisions. Bucking traffic may be considered one of the most dangerous hazards, as a head-on collision often results in death or severe injury to all persons involved.
And from "Traffic Hazards in Philadelphia," in Keystone Motorist (1930):
Outside of the central area, drivers constantly ignore one-way street restrictions. 'Bucking traffic' has become commonplace. This is true, also, of the drivers of bakery, laundry and milk wagons, whose familiarity with neighborhoods apparently gives them a sense of proprietorship of the streets. It is the exception, rather than the rule, to find such vehicles parked along the curb. Usually they are in the middle of the street, and in the case of one-way streets...
From Fire Engineering, volume 84 (1931):
Box 12 as shown is struck at 1:45 a. m. and fire is located, and is plainly visible to fire company as they turn in at B. The driver of leading apparatus uses route No. 2, his claim being that there is no possible rule or local ordinance that can prevail against the State Law covering emergency apparatus, in this case Fire Department. The driver No. 1 argues that the local street rule comes first and he has no right at any time to "buck traffic"—fire or no fire and that he could be arrested and fined for using route No. 2.
As these examples indicate, early use of the phrase is unusually concentrated in the city of Philadelphia, and the sense of the term is not simply "going against the general flow of traffic," but "going against traffic signals or instructions" and even more specifically "going the wrong way on a one-way street." This suggests a notion of head-on collisions as vehicles butting heads.
The early, very narrow sense of "bucking traffic" persists in some Google Books matches at least as late as 1959. From Toledo City Journal (1959) [combined snippets]:
Akron's increasing one-way streets are worrying Fire Chief Gerald Vernotzy. Up to now, Akron firemen have been bucking traffic—that is, driving the wrong way on one-way streets—when emergency demanded. Vernotzy clamped down on this practice.
'Bucking traffic' as 'crossing into oncoming traffic in order to pass a vehicle'
Even in the 1920s, some sources used "buck traffic" in the sense of "go against oncoming traffic" without necessarily implying a violation of traffic regulations. From Delaware State Highway Department, A Report of the State Highway Department of the State of Delaware, 1917–1926 (1926[?]) [combined snippets]:
MINIMUM SPEED The excessively slow vehicle on a heavily-traveled road must be regarded as a serious obstacle to safe driving. It compels vehicles in the rear to "buck" traffic in getting by, and so directly provides the cause for one of the main sources of highway accidents.
From Bus Transportation, volume 8 (1929) [combined snippets]:
Don't try to pass immediately every vehicle you overtake, take your time and pass when absolutely safe. If the highway is congested, drift with the traffic and pass as the vehicles ahead bunch up, two or three at a time. You can make just as good time on a congested highway by drifting with the traffic and passing only when absolutely safe as you can be [by] bucking traffic, and it is much less wearing on the nerves.
From The American City, volume 42 (1930) [combined snippets]:
Taxis do a thriving business at major events and each driver tries to make as many trips as possible before the start and after the end of the performance. One very good remedy for the congestion this creates is to provide a one-way loop route, over which taxis may go to and from the gathering without bucking traffic. Private cars with drivers should be permitted the same privileges accorded taxis, with respect to using a loop whereby a convenient place to discharge passengers may be reached.
From Rogers v. Moody, 430 Pa. 121 (May 21, 1968), a case that arose in connection with a traffic accident in Philadelphia:
The MacMillan car stopped for gasoline at a gasoline station at the corner of Hunting Park Avenue and Clarissa Street, and then started out to turn left to enter into Clarissa Street, to proceed in a northwardly direction on that thoroughfare. After momentarily halting so that a taxicab which was blocking MacMillan's way could back up to allow MacMillan passage, MacMillan looked to the left and saw no cars approaching, his view extending some 200 feet; he then looked to the right and saw no northbound traffic coming from this direction. When he looked to the left again the Moody car was headed directly for him on his, Moody's, wrong side of the road. The evidence supports the conclusion that Moody, moving in the line of the Clarissa Street traffic, impatient with waiting for the cars ahead of him to turn right onto Hunting Park Avenue, drove around them. In so doing, he was "bucking traffic" and moved rapidly to regain his proper side of the highway as quickly as possible. It was during this flanking movement that he saw the MacMillan car dead ahead and the collision inevitably resulted.
'Bucking traffic' as 'driving through congested streets'
From Michigan Roads & Construction, volume 39 (1942):
MacDonald said in some congested areas, downtown business houses are literally starving for business to a point where their value has shrunk to less than the mortgages on them simply because shoppers decline to buck traffic jams and a lack of parking facilities to reach them.
From The Catholic Digest, volume 15 (1951) [combined snippets]:
You can't go from anywhere to anywhere else without bucking traffic; in Los Angeles, motorcars are like waves on the ocean. Looking down from City hall tower or any high point in the city, you can see parked cars everywhere. Whenever there is a big football game in the Coliseum, cars are parked over lawns for blocks.
From National Safety Council, Transactions of the National Safety Congress (1957) [combined snippets]:
Any vehicle that crosses the flow of oncoming traffic to enter a service station is construed to be "bucking" traffic. Experience in Ohio and Michigan shows that an average of 38 per cent of the cars entering a service station "buck" traffic to enter.
...
Why do motorists buck traffic? When a traffic light turns there is an open space in the oncoming lane. If a motorist intends to turn at the corner, the easy, safe path is through the station and the motorist takes this path. Bucking traffic is directly related to the second general principle namely, that the motorist will select the easiest and safest path.
From Ohio Cities and Villages, volumes 5–6 (1957[?]) [combined snippets]:
For the most part our downtown areas have no room for more cars without wholesale destruction of buildings and huge capital outlays for parking facilities. The cost to the public to construct roads to carry those cars from work to home is fantastic. The time spent behind the wheels bucking traffic is wasted—and our nerves are jangled. Fumes from the gas exhaust pollute our skies. Diesel busses too add to the confusion as well as pollution.
From Landscape Architecture, volumes 48–49 (1959[?]) [combined snippets]:
Why is it that most families, out for a Sunday afternoon drive, follow the byways rather than the highways? Because the whole family gets more enjoyment from such a drive, rather than bucking traffic all the way. The children are fascinated by farm animals. Mother looks, sometimes in envy, at the charming dooryards of country homes. Even father, driving, gets relief from constant tension found on the highway.
From Réalités, issues 260-265 (1972) [combined snippets]:
In management's eyes, "flextime" makes Heinrich more efficient. He no longer shows up with nerves frayed from bucking traffic jams. If he feels lousy, he doesn't call in sick and miss a day, he just comes to work somewhat later. Flextime has cut absenteeism, increased productivity, reduced paid overtime, soothed nerves and probably avoided a few ulcers. For employees like Heinrich, it has lowered the high pressure of industrialized life, slowed the "rat race," and made work uniquely more pleasant.
From Meni Koslowsky, Avraham Kluger & Mordechai Reich, Commuting Stress: Causes, Effects and Methods of Coping (1995):
For example, while an hour train ride may involve more time and distance than a 35-minute commute by car, for some people, the train ride may be perceived as less stressful because they would not have to buck traffic or fight to find a parking space. For others, time alone in a car might be perceived as less stressful than being a passenger in a train (or, especially, a commuter subway with other people).
From John Simonds, Landscape Architecture: A Manual of Site Planning and Design (1998) [combined snippets]:
The early abandonment of the industrialized city in search of greener pastures gained momentum until it became a rout. The migration was given impetus by the coming of the automobile and the expansion of the highway network. Moreover, as families and businesses pulled up stakes, city taxes were raised to compensate for the loss, while property values declined. The outward flight has continued until now many who work in the city and live in exurbia must spend hours a day in bucking traffic as they drive to and fro. It is only recently that the balance is beginning to tip. As suburban communities become commercialized and lose their appeal, and as revitalized cities become more attractive, there is an increasing back-to-the-city movement.
Conclusions
Since at least 1846, buck has had the informal (but now standard) meaning "to defy, resist, or oppose." When the phrase "bucking traffic" first arose (by 1919), it seems to have referred to disobeying traffic indicators—semaphores or traffic signs—and in particular referred to going the wrong way on a one-way street. An allied meaning soon arose: crossing into oncoming traffic in order to pass a car or other vehicle in front of one's vehicle. This could be lawful (if done cautiously) or unlawful (if done recklessly). A final stage in the evolution of the term evidently arose by 1942, conveying the sense of simply fighting heavy traffic, whether one is in one's proper lane or not.
Best Answer
If you are talking about traffic in general, as a common scenario, not specific to any road or incidence, then you can ommit "the". Example: "You often spot some people going against traffic on the streets near schools, which is very dangerous"
But when you are talking about a particular situation where the story happened and you want to mention traffic on some road, then use "the" to elaborate the incidence ("The" traffic which you talk about Example: "Police patrol saw the guy when they were passing by George Street. He was seen going against the traffic."