Hi Ebza
Hang in there! I had a mare that was an absolute nutter. She was my second/third horse and I got her really cheap, (and after a while I realized why). She used to do the same as what you describe yours as doing.
My mare avoided any contact with the bit, but when she did make contact she would grasp it firmly between her teeth(so to speek) and bolt, or she would try putting her chin on her chest ???? and then she would rear. A small warning rear first and then a doozy for the finish. She would always rear when in company and was 'last' and when you asked her to do something she didn't want to do.
I had her checked over numerous times and tried numerous bits and contraptions people had suggested, (I was new to it all back then).
After two years of putting up with the crap, I ended up putting a hackamore on her and tada!....different horse.
I am not suggesting you do this, but I am suggesting it could be something simple.
BUT please get a pro trainer to sort it out for you. I have seen a few people get "squashed by rearing horses and it aint pretty!!
Good luck and don't let your neddy get away with it for another day!
Cheers
Jo