Not to pile on about contacting the professor, but pickles50's post made me think of something. My friend works at a university as an academic coordinator (sort of recruiter, advisor, teaching assistant, etc. all rolled into one). I would say her number one complaint about students is that some aren't proactive about solving their own problems.
For example, one class she was helping out with had group projects, where each group was supposed to work with a professor to explore a research topic. Sadly, one of the professors was flaky and never got back to the students, even though they tried to contact him several times. However, the students didn't let anyone know they were having this problem. Instead, they turned in a half-baked project at the end and then, when they got a bad grade, reported that the professor refused to make time for them (and showed the emails supporting this). My friend's opinion was--well, that's horrible of the professor and we're going to speak to him about it, but why didn't you tell us this earlier, when we could have done something about it?! So the bad grade stood.
I don't know if students aren't used to showing initiative like that, or if they think they'll just be seen as whining to the teacher, or what. But in the "real" world there are ways to let a higher-up know about problems in a professional way that should not reflect badly on the person having the problem. So, add me to the chorus of people who think the OP should contact the professor with a professional, non-emotional email explaining why she doesn't want to be in a group with Moochette (my fave name for her).
"Professor X: Regarding group project #1, Ann Miller, Joe Brown, Paul Jones, and I would like to form a group. [copied them on email] Another classmate, Betty Smith, has told me she asked you to put her in a group with me. I request that Betty Smith and I not be assigned to any projects together. Based on my previous interactions with her in multiple classes and on her answers to the 'getting to know me' class assignment (see attached), I believe she will be unreliable and not contribute meaningfully to the assignment. I take my coursework seriously and would like to work with others who feel the same way. Sincerely, OP."
Not guaranteed to work, of course, but if they're assigned to a group together anyway, the OP can send another professional email requesting guidance on how to document each group member's contribution.