J.W.
My middle daughter was a biter. It started when my 3rd child was born and escalated intensely when the new baby started to require more than holding/sleeping. It's my opinion that it gets even worse when the new baby becomes mobile (needs mom to look at her/him & mom can no longer be watching big sister/brother all of the time).
Anyway, it continued until it was done (a phase). The one thing that helped the most and was something different than the other stuff I'd heard was that the behavior was telling me that she needed me. She was exceptionally good at talking early, so this seemed unlikely to me. I thought she should be able to tell me, but truthfully, she was unable to verbalize her needs.
What my friend did with her son was pick him up and hold him and say "Your behavior is telling me that you need mama. If you need me, I need you to tell me (or make up a signal). Biting is NOT okay."
I also tried not to stay @ playgroups "too long". There were some subtle signs in the way she moved and interacted w/the other kids. She'd start to move away from the group a little or seem to be just a little "faster" in her movements.
Sometimes, I would offer to hold her or to play with her for a few special minutes when we'd been somewhere for a while. It seemed like she could go back to playing with the group for a bit after that, but really, it was usually time to go. I also found that she is a person who needs time alone to be by herself and that she enjoys spending more time at home (my oldest & I are "on the go" people).
Good luck! It really is such a short time that they need us so much.