I agree with Kevinshorses, this sounds like an issue with how the bridle is being put on. Not necessarily bashing the teeth with the bit, but not being totally effective with bridling. I know several horses who will run backwards and fuss at bridling unless its done fairly quickly and tidily, in which case they are gems. Also, watch how you're putting the headstall over her ears. If she's anticipating having her ears stuffed into place, she may be reacting to that rather than bit discomfort.
Was this a sudden change, or has it been building for a while, slowly becoming less and less manageable? If it's been sudden, figure out what changed around the same time as your mare's attitude. There's always a reason. Have her teeth been done recently? If her teeth are bothering her that can be a definite reason for her behavior.
A change of bits may help you, some horses can be pretty choosey. Rubber bits are big and bulky, and a lot of horses just don't have the mouth space to carry that big of a chunk around comfortably. If the bit is hurting her (i.e. she needs her teeth done or something adjusted tack wise), changing metals won't help you much.
I'd love to see what she's doing and how you're bridling her. It's hard to describe in print, but I see a lot of fussy horses instantly bridle better if you hold the cheekpieces in your right hand (assuming that you're standing on the left side to bridle), "feed" the bit to her while cradling the bridge of her nose in the right hand with the headstall, and, after the bit is in, taking the crownpiece in your left hand, and gently fold the ears under.
Hope that was somewhat helpful to you, and good luck!