If it is an organized playgroup (through some organization like a Mom's Club), you can talk to the organization about it. We had a similar situation, and the organization's rules were that the biter had to withdraw from the playgroup until the behavior stopped. It may make the mom mad, but it seems to reason that the one causing the issue should be the one that cannot participate. (Although my children are 10 and 12 now, and that is not always the way it works even in school!) The downside to this approach is that it doesn't help the biter learn how to stop this behavior and understand it is wrong.
If it is not an organized playgroup, you might want to talk to the other parents to see if they have the same issue, or even in explaining to them why you are going to have to not participate for awhile, might spark that conversation without you having to bring it up. If the other parents have the same problem, you might want to approach the mom as a group. If that is too forward, you might want to see if you can get together with some of the other children one on one, instead of in a group.
The third approach, which may be the hardest to do, but hopefully the more effective - is to have a heart to heart talk with the mom (especially if you do get along normally). She might not be making a big deal about it because she is mortified, and doesn't want to draw more attention to it. Or she may just keep hoping it will pass. But it won't just go away if the child is not given the message that something is wrong. You could approach her like it is a problem that both of you could solve. That you know it could have just as easily been your child who decided to experiment with biting, and you want to know if you can help. Have a plan for what happens if her child bites (They get removed from the playing for a determined amount of time, and the one bitten gets a huge amount of attention from the rest of the moms, in view of the biter). But to have this method be effective, you have to come to her like one concerned parent to another, as opposed to being on the defensive about what her child is doing to yours (which will be really hard). If the other mom is agreeable to this, it would be a win-win for all involved, her child learns not to bite, and your child can enjoy her friends without the fear of getting hurt!
I hope that helps!