Do pros slide the bridge hand into play on (most) shots? They do not.
You will often see newbies and low-level league players get into the stance with a very large tip gap, then slide their stroke hand forward to close this gap--which ruins the angle of their shooting arm before practice strokes are taken.
Some stronger players correct large tip gaps with the type of bridge hand slide you described, which slide action tugs the stroke hand a small distance forward--not as bad as moving the stroke hand directly, but bad for the stance regardless.
IMHO, the correct way to tighten a tip gap at address is the feet--standing closer to the balls to begin the stance process.
This is true in all stick-and-ball sports, for example, we tell the batter to stand closer to home plate, and would never tell them to instead stand too far from home plate then stretch their arms an added distance to swing and contact the baseball.
I believe the pool instructor was correct unless the stance and all else were superb after the slide for all shots during the lesson--something I've not before seen with bridge hand sliders.