She hates bits. All bits. D ring, O ring, french link, small diameter, wide diameter, happy mouth, mullen mouth - you name it, she hates it.
Has she learned to yield well to pressure in all ways, reliably WITHOUT a bit? If not, that's where I'd start. Then when first introducing a bit, with Cherie's advice in mind, just let her getting used to wearing a comfortable one first. Don't start asking her to respond to it until she's desensitised to having it there in the first place.
no pressure, bit adjusted correctly in her mouth (one soft wrinkle).
The 'nutcracker' effect of a regular snaffle can be quite strong & 'one soft wrinkle' is often enough pressure - too tight for her. Just because your hands weren't on the reins doesn't mean there wasn't any pressure. I would also suggest that she wasn't ready for a bit, that it seems she needs a bit more desensitising first.
Worked through it and got her moving, but she had her mouth gaped wide open with lips curled back and head between her knees for the first week.
Can you remember the first time you wore a tie, sunglasses, a skivvy? It was very irritating, but eventually you became desensitised to wearing these things. That's why you don't start with actually using a bit - & one reason I think it's best to teach a horse to yield to rein pressure without one to start with. Allow her to wear it, fuss with it, eventually be distracted by something, then take it off when she's not fussing. I'd do that until she's no longer bothered before thinking about using it for communication.
I was really surprised that a few weeks of steady work didn't solve the gaping and head tossing. (I had her wisdom teeth pulled and teeth floated as soon as I got her - no physical reason for her aversion to bits that vet can see).
It's great you've attended to her teeth(how long ago because I gather you mean wolf teeth pulled & they can sit right where the bit is & it takes months to heal), but I wouldn't say there's no physical reason for her aversion to an uncomfortable piece of metal in her mouth, especially if pressure was applied to it, especially if she hadn't first learned how to yield to pressure well.
Each lesson I put on a D ring snaffle with a rope cavesson underneath so she can open her mouth a little, but not gape - and we lunge or drive at the walk and trot with an occasional canter.
So as suggested, I'd ditch the snaffle for a gentler, more comfortable bit. I'd also ditch the cavesson or any other equipment that forces her & gives her something else to resist & fight with. (I'd also not want to be doing much lunging at all with a youngster, at least not at a fast trot or canter.)
Then while she's wearing the bit I'd ask her to do some yielding of hindquarters & the likes, loading in trailers, obstacle courses, go for walks(lead clipped to halter) & meet other horses, picking up feet, etc, etc, basically anything that is low stress(she has already learned how) that will take her mind off it & that doesn't require any pressure whatsoever on her mouth.
but now it takes about 10 minutes of a walk/strong trot before she carries the bit calmly. She can make a couple circles and then regresses and goes back to curling her lip back, head shaking, pulling, opening her mouth ....it takes about 35 to 45 minutes per session
Oh OK, missed that bit when I read the rest, so that's really good & sounds like you are actually a bit further ahead than you feel. Aside from 35-45 minute sessions, especially when talking lunging & fast speeds, sounding WAAAY too long. You need to negatively reinforce(remove the discomfort) her for the Right behaviour, rather than just pushing on until she tries something else because the 'good' behaviour didn't work - getting reactive about it again. So when she carries the bit calmly after 10 minutes, THAT is when I'd stop work & remove it. What she needs is practice at this behaviour working for her.
My neighbor was watching and yelled across the fence - "that one isn't going to GIVE you anything. You are going to have to earn it with her." ...I need to set her up for success - try not to get frustrated, try not to get mad at her bit issues, and just give her the time to get through it and get her to respect the bit and the person on the end of the line...
Very good points!