I predict you're going to get a huge range of responses here, from "Don't interfere in any way and let her go and handle it herself" all the way through to "Keep her home." This is the kind of situation that's tough to judge without knowing your daughter well and without knowing the exact nature of the bullying.
YOU know your child best. Would she be relieved if you said you were going as a chaperone? Would she be relieved (probably only secretly so) if you said you were keeping her home? Or would she be mortified at the thought of having you on the trip and would she see you as hovering? Would she see it as "Whew, I can finally enjoy this trip" or instead as "Oh no, the other kids are going to think I need my mommy there and I'm not mature enough to handle things." Which ?
Think through these things based on what you know of your kid-- and talk to her about it! Don't be afraid to sit down with her and say, "There are some options here" and walk with her through those options. If she's fairly mature and can talk about the bullying openly she may be able to come up with her own ideas about what would work best. She IS right that she should not have to pay a price because someone else is behaving badly but she also deserves not to have to have a miserable time.
Are there other moms going? Do any of them know your kid well and would you trust them to keep an eye on things? (I think that's asking a lot but again -- only you know the people involved.)
Would it help to see the principal in person and emphasize that it is unfair for kids who are being bullied to be expected to put up with it on an overnight trip as well? It seems the principal is well aware of this girl's issues -- would the principal consider arranging for the girl who is the bully to sleep separately from the other girls, with an adult chaperone, for instance? (Yes, yes, it isolates her and that's not good, some would say, but it may be the shock she needs: Behave this way and you will be isolated for others' sake.)
If it were me, with MY particular kid, I would simply tell the school that I was going as a chaperone, period. My daughter (also in middle school) is the kind who would want that, in this situation. But my child isn't your child.
You already know that you are "not OK with letting her go and handle this all on her own" so don't let her go and handle it on her own. You already know that the principal, while not exactly embracing having you come along, has said that if you insist she'll allow you to go. So -- if your daughter is OK with it, because she should have a say here -- insist. Not in front of your kid or other parents, but with the principal.
Be aware that you might be talked about by some other parents as being a "helicopter mom" or as hovering or coddling your child or "not letting her grow up." So what! You know her best and know what she needs. If this were high school it might be different, but if she's in sixth or seventh grade middle school, do what your gut says. Just be sure your daughter is OK with it too and won't resent your being there. If she is really balky about your going, and doesn't want to stay home either, reconsider and arm her with things to say when bullied.