Shoot the ground directly in front of the opponent. Since its a scatter effect it will work best against big targets. It's a little tricky to do, as the idea is that the arrow will impact the ground so close to the opponent that all the scattered arrows don't have a chance to go into anywhere else. I would recommend loading up the training grounds and trying it on the training dummies to get a feel for how it works.
Edit: Here's a crude drawing of what you're trying to do. The red line is the scatter arrow. It's like you're firing a shotgun shell at the point of impact so the closer the impact point, the more effective it is.
Zenyatta does have a somewhat unique playstyle. His squishiness makes it so he needs to stay out of the open and stay near his tanks, preferably a Reinhardt who can use his barrier to shield Zenyatta and help make up for the squishiness.
Zenyatta's orb of Harmony heals 30 health per second, which is lower than Mercy's healing, but has a longer range, as an orb of Harmony will remain on an ally so long as Zenyatta has line of sight of that ally. One thing of importance is that Zenyatta cannot send his orb of Harmony through an enemy shield or barrier. Generally you want to throw this on whoever is taking the most damage, usually an offensive or tank hero.
For orb of Discord, this like orb of Harmony can be thrown at a range of 40 m, and remains at any distance provided that he keeps line of sight. Orb of Discord provides 50% bonus damage from all allies against the target with it on, so it is good to put on the enemy tank to help burn them down, or on an enemy offensive hero to make sure they die quickly before getting damage out. Note, losing line of sight for 3 seconds will remove the orb, and it cannot travel through enemy shields and barriers.
Zenyatta's regular attack does quite a bit of damage (35-175; 35 per orb in charged shot and 5 shots total; regular fire deals 45 per orb), especially if you have an orb of Discord on the target. His charge shot is great to use when ever someone gets close range and needs to be killed as quickly as possible such as a McCree or Reaper. His regular fire is great for wearing down the enemy from a distance, though it does have a travel time, so make sure to lead a little. Times when you should charge his alt fire would be, when McCree uses his ultimate Deadeye, when Reaper is Shadow Stepping at a destination, when Widowmaker is sniping in the distance as you want to not expose yourself to snipers, while Mei is in a Cryo-freeze (fire once she unfreezes), when Zarya's barrier is on someone (use it when shield wears off). You can also use it to help burst a Bastion or Torbjorn turret by charing in cover and popping out to unleash all 5 orbs at him.
His ulti heals for 100 health per second to nearby allies and makes him invulnerable to damage for 6 seconds. While using his ult, you can block a number of enemy ults from hitting your team such as Blocking enemy ultimates most notably: Reinhardt's Earthshatter, D.va's Self-Destruct, Mei's Blizzard (the line of sight starts with Mei's Blizzard Drone), Junkrat's Rip-Tire, McCree's Deadeye, Reaper's Deathblossom, Pharah's Barrage, Bastion's Tank Form, Roadhog's Whole Hog. The main uses for transcendence are for initiating strong pushes, to simply save yourself, to counter pushes done by the enemy, and to massively heal your team.
Best Answer
McCree is great at medium to close range but not that good at medium to long range.
I treat McCrees almost like I do Reapers: get out of their close range high-damage zone and you'll be fine.
Genji is not a good counter for McCree*; use any hero that'll allow you to do decent damage from out of flashbang range.
Sniper heroes (Hanzo and Widowmaker) are good at this, Pharah can conveniently drop rockets from above on him, Junkrat can also keep him at bay with his traps. Of course turrets (either Torbjorn's or Bation's) are great to keep any hero away.
Every hero has something that they're great at and it will be hard to defeat them if you go up against their best game. In McCree's case, it is dealing damage at his flashbang range. Do your best to avoid that and you should be fine.
* Genji is not a good counter because he usually needs a combination of some of his Shurikens, melee and Swift Strike (occasionally two of these will suffice) to kill another hero fast enough. Genji doesn't do well with long battles against other heroes and this combo will most likely alert McCree to Genji's position and get Genji in flahsbang range before he can kill McCree. This is everything McCree wants and it'll force you into the terrible baiting battle you described.