My sister's mare started having bridling problems. She was never being ridden so my sister gave her to me. I took her on a test ride and tack up and bridling was perfect. When the ride was over I started pulling off the headstall and as soon as I got it past her ears her head shot up in the air and she darted back 5 feet. The bit was dangling from her mouth and she was really panicked. Next few times that I bridled her we had this problem. What I think is that at some point my sister had ripped the bit out of her mouth and had banged her teeth. So, in anticipation of her teeth hurting she would throw her head up, but in doing so she would actually get the bit hung up on her teeth and made the problem worse. This mare had no idea how to drop the bit out and was scared when it moved in her mouth.
Very soon after she stopped letting me put the bridle on at all. Did giraffe neck, looked at the ceiling, moved her head from side to side.... she just didn't want to deal with it. I know she was avoiding the bit because she wanted to avoid the fiasco in taking it off. I got her teeth checked out by the vet. (The vet bridled and unbridled her and checked the fit and everything) He told me she definitely is just psyching herself out.
I bought a rope halter, taught her to give to poll pressure and used it as an aid in keeping her head down while I bridled her. I also would use the same poll pressure when I had to take the bit off teaching her to keep her head down and open her mouth to let the bit out. She made really great improvements but it was still slow.
Recently I bought a new bit. This one has a dog bone mouth piece instead of the nutcracker she had on her old snaffle. She seems to really prefer this. She has a low palette so i'm pretty sure her original snaffle was bothering her as well. Now she's perfect about taking the bit and has not needed for me to put pressure on the halter. She drops it out relaxed when I take it off too. I still have been using a halter just in case, but I don't think I will need to for much longer.
If I were you I would definitely use a halter to work on bridling but I would also look into trying different bits for her if possible. One of my mares seems to really love her bit sometimes. She has her head down looking for it before I'm even ready to slip it on, it would make it easy on both of you if your horse is comfortable with their bit.
If you don't want to ride with the halter underneath smrobs made this really good video