"Bow is OP because I don't know where the shots are coming from and it hits so hard!"
See, if you don't know where the shots are coming from, that means you've been flanked. Noise or no noise, you're at a severe disadvantage and will likely go down no matter what. Hell, some noisy weapons outperform the Bow when flanking. Hunting Rifle users get all the time in the world to line up a headshot (and it's far easier to do so with it than the Bow) while Burst Rifle users, already major threats in direct firefights, will laugh as they score up to three easy headshots on you (as if they don't get enough of those when not flanking). Nevermind the purchaseables which'll wreck anyone faster than the Bow ever could.
"The Bow is just too fast! I don't stand a chance in a firefight!"
No, you do stand a chance and that's because it's not very fast. At least, it's not fast on the first shot. It has a slower draw time than all of the firearms and is more difficult to aim due to the lack of a scope or reticule, forcing Bow users to spend more time than the average player to line up their shot. You, on the other hand, can spend less time. If you realize they haven't drawn yet, draw first. They try to draw, you shoot. Bow users suffer from much more damage wobble than others, making it nearly impossible for them to win if they've been shot.
Their advantage comes in once they've drawn and lined up their shot. If you've fought Hunting Rifle / Military Sniper users, you'll know that trying to fight one who set their sights on you is just like asking them to blow your brains out. Same applies to Bow users. Popping out is just asking for trouble. Not as much trouble as they aren't as likely to score a headshot, but it does happen. Even if not a headshot, once you're hit, you'll only stand a chance if you're using a rapid-fire weapon and that's if they're sufficiently out of cover. They have no need to adjust their aim anymore. They just need to ready the second arrow.
Point is, learn when to back off and learn when to stand your ground. If you learned against standard firearms, I don't see why you can't learn against the Bow. When you back off, you can heal or, hell, if you're not hit, you can simply wait for their arm to tire and force them to back off after.