Is there a reason you want to blow dry? Our pups coats are short so we dry Bandit off with a towel and let Nala dry herself off with a towel (we put it on the floor and she rubs herself off on it like crazy... very fun to watch

)
As far as biting while brushing him, could you give him a very special snack like a bully stick so he views brushing as a good time and his mouth will be occupied so he can't bite?
Good luck