Use predictive AI to aim your ADS
Other answers are correct. There is no way a laser can wait for someone to pull a trigger and have time to respond by intercepting the bullet, but a much more reasonable expectation would be a system that uses cameras and other sensors positioned around your body that feed into an image recognition AI to predict incoming threats and aim your lasers BEFORE the bullet it fired. If the AI sees someone turning their gun towards you, or a grenade land nearby, it can respond by aiming the lasers to intercept the predicted angle of attack.
This makes all of the concerns regarding how quickly your laser needs to aim or time required to power it up a non-issue because as long as your ADS can out-draw an attacker by reading body language, you have eliminated the time it takes to arm and aim vs when you only start to respond once the shot is fired. So your response time is then reduced to how long it takes a computer system mounted to a high speed camera to respond to the mussel flash which could easily be less than a thousandth of a second. The bullet could still be within inches of the mussel by the time the ADS fires in response. So depending on just how handwavy your laser themselves are, this system could potentially be effective at ranges of just a few meters.
As for accuracy issues...
There is really no rule saying a future tech society can't make a mini orb laser accurate enough to directly hit the bullet, again, using predictive AI, you should be able to map not just where the bullet is, but where it will be so you can hold your laser on target, but what if you don't want this level of auto-aiming technology in your setting?
As it turns out, you don't actually need to hit a projectile for a laser to be an effective ADS. If you base your lasers on the Boeing Plasma Shield concept, you just need to shoot somewhere in the path of the attack, you don't need actually target the projectile itself.
Instead of firing a single laser to try to burn away the bullet, you could fire a set of lasers that converge in the air between you and the enemy just before he fires creating a mid-air plasma burst. This uses less power than is needed to make a viable laser rifle (which solves internal consistency issues), and less accuracy than is needed to directly intercept a supersonic projectile. The plasma burst can do a wide range of things including blocking enemy lasers, overwhelming enemy sensors, visually blinding the enemy, and/or creating a shockwave that can detonate missiles and deflect shrapnel.
The big drawback here is that it will not be able to stop bullets fired at close quarters, but long-ranged sniper shots (the kind where wind speed needs to be taken into account) can be redirected by enough to miss you if it has to fly through a plasma burst somewhere far enough away from you that the slight change in angle would compound into a major offset.
In this way you can use lasers that may not necessarily make for a good primary weapon, but still able to protect you in battle.