I'd reintroduce a bit with a soft rope instead.
Even if she does get worried, clamp on, throw her head, etc, it's not going to hurt her mouth.
Use it the same way you would a bit, you can either just put the rope in her mouth or tie a short stretch to your bridle so it is the exact same. Ask her to open and accept the rope into her mouth, while she is relaxed with her head relatively low, then slowly bring it out of her mouth. Repeat until she is quiet with it.
once you go to an actual bit, your problem should be all but gone and you won't have to worry about her hurting her teeth.