Sounds like disrespect and some barn sourness. She has learned how to avoid work by tossing her head, so I don't think that any kind of bit or hackamore is going to stop the tossing. She more likely has holes in her training. I am not sure using a green as a lesson horse is a good idea even on a lead line. When she starts with a temper tantrum you really need to hustle her feet, and make her uncomfortable for showing her disrespect. Since your pregnant it would be safer to do it from the ground you have three seconds to correct her behavior, so you would have to get off fast and set her feet to work. Lunging with lots of changing of directions works well, so you would have to ride with a halter and lead rope attached so you can grab it quickly. If you keep the end of the lead rope through you belt loop you can grab while your swinging off and send her to work. Personally I love my mecate reins I can jump off and put a horse work in two seconds. And while your riding make sure your engaged and not letting her go on autopilot until you have a problem. Do circles, shoulder in/shoulder out, lots of transitions keep her thinking about you so she does not have time to think about doing the wrong thing. They can only think about one thing at a time. That you can do a ORS is good, the bolting is bad, she has learned how to get away from you. If she bolts then stop her and put her feet to work she needs to know your in charge of her feet. For the barn sourness work her hard with lots of changes of direction where she wants to be and then let her rest and catch her air away from her magnet. You will probably not be able to tire her out to easily so you have to rely on getting her to use the thinking side of her brain instead of the reactive side. Since you pregnant not sure trying to fix this is safe right now but maybe you can find someone to help you, besides the person who wants to use a tie down.
As long as the bit is a good fit in her mouth, then I would adjust the bit to max. 1 wrinkle and I actually prefer no wrinkles that way when your on a loose rein they find relief, from all the pressure.
Good luck and be safe