Good luck with your puppy class! It's a really great experience, both for the dogs and the owners. I took Milly to some extra classes after she passed her puppy award, just because she seemed to enjoy it that much!
I feel your pain about the biting
Absolutely nothing seemed to work for mine but persistence and discouragement does eventually pay off (or did she just "grow out of it"? I don't know, but it's a long haul to get them to stop nipping!)