Two issues: one is the bit fit and one is training.
Is the bit big enough for her? I suspect it is too short and no matter what you do, it will always rub. Measure her mouth, measure the bit. I always allow another 1/2" width which give 1/4" on either side. Use a piece of clean rubber tubing (a chunk of old garden hose works well) to measure. Put the rubber hose in your horse's mouth and mark both sides flush with her mouth. Measurement + 1/2" is your required bit size.
Changing the bit for more power control as opposed to more finesse control is not something I would do. She is still on the young side. It sounds like she missed a bit of training or it hasn't been reinforced. Work at halts at a walk until those are down pat, then move to trotting and transitioning down to a walk and a stop. Don't move to the next gait until the first is solid. Ensure that your riding is meeting her training -- does she respond to your seat or only to your hands?
Until you have the stop solidly in place, you won't get more finesse anyway. I am always a fan of milder bits. You might consider D-rings instead of O-rings.