M., you've gotten a lot of advice, so I'll try to keep this short. I second the recommendation about "Queen Bees and Wanna Bes" and would add also another book "Odd Girl Out." Not all of it applies to your child but lots will.
Yeah, you should probably talk to the mom, but don't expect much. Go in there with very specific things: dates, places, exact quotes, witnesses, etc. Then say, "What do you think we can do about this?" Or, alternatively, say, "This is what I plan to do, on MY end." If you put yourself in the position of requesting that she solve the problem, a) she will get defensive (she'll do that anyway, it's unavoidable) and b) nothing will happen.
Finally, the advice that your daughter just walk away from encounters is one of those things everybody says, and it sounds good, but it's not always the best way. There's a middle ground between walking away and getting in a fight. Sit down with her and role-play some possible comebacks. "I know that's not true, and YOU know that's not true, so why would you say that?" Or, "Man, you must be really bored today, to need all this drama." Or just, "Oh, PLEASE" (and roll her eyes). Or play dumb: "Let me get this straight: X isn't talking to Y because Y thinks I said something nasty about Z? Can you walk me through this again?" (repeat as necessary, until "Hannah" realizes she's being had.) Walking away can be good in some instances, but many times it just rachets up the teasing/bullying or whatever, because it's a challenge to the perpetrator to keep trying until they DO get a response. A quiet, level-headed verbal response can often work wonders. My 11 yr old was dealing with a bully at camp this summer who just kept saying snarky things to her--drove her to tears--until we did this. The next time it happened, the bully says to my daughter something along the lines of "WHY are you wearing THAT?" and my daughter said, "Oh, Megan, you know, my plans about what to wear changed suddenly last night, and I didn't have your home phone, so I couldn't call and let you know." The whole class laughed and it shut Megan up for the rest of camp. It was a line my daughter and I had rehearsed together before the fact. When it comes to bullying, kids need a whole tool box of options, not just one.
Also: look up your school system's policy on its website, and contact the school's parent liason, if they have one. When it comes to bullying, schools are programmed to deal only with physical altercations (and not even effectively with those, lots of times). Verbal bullying of the type girls do tends to be off their radar screen unless you put it ON their radar screen. In my daughter's case, she was never told she could file a written complaint about some other kids--I had to find it out on the school's website. When I mentioned this, suddenly I got a whole lot of attention; educators are VERY sensitive to paperwork requirements. We never used this mechanism but it was good to know it was there. Good luck