just my opinion, but if the horse is rushing, she sounds a bit nervous and lacking confidence. I would stay at very easy low jumps, cavaletti, etc., and take as much time as she needs to relax. My old TB mare was also nervous about stuff, it varied from one day to another. Some days she could be 'challenged', and other days she needed do very routine, easy work to calm her.
I also went through about 20 bits trying to find the 'right' one. The 'improvement' would only last a few days or weeks, and we'd be having troubles again. It's all in the training, your seat, legs, and hands. After awhile, the more I changed bits the worse she got. She actually went the best in a old full cheek plain snaffle, and in a noseband with no bit at all.