Here's what you're trading for the alertness feat if you don't take the abil score upgrade and instead take the feat:
- +1 to damage
- +1 to hit
- +1 to AC
- +1 to Dex saves
- +1 to Dex checks
- +1 to init
The question then, ultimately, becomes, is +5 init (net +4), no surprise and no advantage on attacks against from hidden opponents worth it.
The latter two features are very dependent on your campaign and DM. Surprise should be a fairly frequent occurrence on both sides of combat, but that still depends on how willing your DM is to allow it or stage his monsters to have them obtain it (and kind of how cautious your group tends to be). Monsters attacking from hidden is another one that really depends on your DM, you group and how well you guys are at nosing out monsters from the shadows.
So ignoring those two items since they are DM and campaign dependent (and thus can't be weighted objectively), the question then becomes, is +1 to Dex more or less beneficial over 4 levels than +5 to init.
For pretty much any character other than the Assassin Rogue, I'd probably argue that they should take the stat upgrade early, the feat at L8 and then the last stat upgrade. However +5 init has amazing synergy with the Assassin Rogue and you're going to get a ton of mileage out of it.
If you're already at 20 Dex (if you managed to start at 20, or 18 and are at L8), then there really isn't any stat upgrade that is worth taking over this feat (though there may be better feats). Rogues are skill monkeys, yes, but +5% in a single ability set of skills is not worth the +25% to initiative and other features o this feat. The only one that would be worth considering at all is Con for the extra HP, but it's really not that many and you're better of boosting your damage significantly.
Take the feat at L4 (or even better, play a human and take it at L1).
The bonus of ASI is a one-time-only increase to ability scores:
When you reach 4th level, and again at 8th, 12th, 16th, and 19th level, you can increase one ability score of your choice by 2, or you
can increase two ability scores of your choice by 1. (PHB, various
pages, emphasis mine)
It is not always "on", but happens at certain points in time. After you get those levels, you are not under the effect of the ASI anymore. Thus wild shape will replace your increased scores.
Best Answer
Your low-Dexterity character is a klutz. You'll want to demonstrate this in minor ways at first, to let your party get used to the idea.
Describe how your character is admiring apples at the fruit cart in the town market... and then drops one into the street, where it gets crushed under the wheel of a passing merchant's wheelbarrow. The fruitseller, unimpressed, tells your party, "That'll be a copper." No big deal for adventurers, sure. Do this a couple times. Maybe you accidentally knock a small animal cage open and have to catch the animal, pay for it, or prevent it from causing further market mayhem. Maybe you drop a dagger at the blacksmith's... luckily, no harm done, no fingers lost... but the blacksmith is now annoyedly huffing at your party; try haggling after that.
Then, after a couple successful adventures, offer to go potion-shopping... and see if your party will let you go alone. Say that somehow, they let you go. Roleplay being drawn to the bottle of a potion on display. Mention that you want to pick up the bottle to examine the craftsmanship of the glass, and how it refracts the light... and see how fast your companions interject with a "Don't touch that!"
Let's not talk about that one time, in the dungeon, when you were near the cauldron of boiling acid.
Or, maybe your character knows he or she is a klutz. You offer to sit in the cart instead of taking a turn clearing the trail ahead. You stand back when it comes to the heavy lifting. "Oh, it's best for all involved if I don't," you say, when the fighter wants you to open the door so they can charge in, or to the rogue who wants you to hold onto something so they can disarm the trap. You get a reputation for being lazy or too fussy, but really you know what'll happen if you lend a hand...
Did your character grow up rich? Maybe you are fussy. Maybe you've had others to do the manual labor for you all your life. You'd rather your party members do things for you, too, because old habits are hard to break, but you realize that it's not their job. But you're becoming really good at making excuses and being really polite, finding new ways to phrase your requests every time it comes up. Your party is going to catch on eventually, so expect to soon be on your own with these things, and like it.
Maybe your character overcompensates. At festivals, you makes a beeline to knife-throwing games because all you need is a little more practice, obviously. You never win anything, of course, unless you get terribly lucky. Then you let everybody know of your exceptional deed! This inflated self-recognition happens in combat, too. You roll a natural 20 (or whatever the equivalent is in the system you're playing) and suddenly your character is commenting on what a great strike that was, did you see that? You keep going on about it for a round or two, until your party reminds you that you're still in combat and can it wait, maybe, until everyone is out of danger? Okay? Please?