What sort of bit is it, and what was he in before?
Having asked that, I would say that bits aren't like girths that need tightening after a bit - it should fit at the right height in his mouth, which was either before or after you lifted/it. I'm guessing that if you took up 'slack', then until you did that it was hanging too low, and he was chomping at it with his teeth.
If it is in the right position in his mouth (put it on, open up his mouth and look where is is sitting), and assuming that it is not a very severe bit, then you shouldn't have to do anything else. You should just ride him