Do you at least have sight of the shooter, at a reasonably high resolution? A lot of time can be shaved off the interception if you don't worry about tracking the bullet itself, but instead calculate its trajectory and launch time based upon the shooter's aim and when they tighten their finger on the trigger. Launch your interceptor in the split second after they commit to the shot but before the bullet leaves the chamber, and you have time to launch a larger mass to intercept it - even a stream of projectiles to help ensure a hit.
Wouldn't work. Bullets have too much spread due to imperfections in the bullet and the rifling which acts as minor limit on accuracy, but matters much more when you are trying to hit a cubic centimeter target in the air not to mention the motion of the person firing is not smooth either. If you are close enough to predict these things, you're probably on the ledge with the hero.
ETA: Looked up at the AR-15 tests, its cone is a mere 1.1 inches over 100 yards so that part is probably fine for the distances were talking. The shooter's motion would still probably throw you off too much though.