I think it depends on the horse. From the way she reacted to the bit I think you should stick with a hackamore if she goes well with it. I've ridden heaps of horses in hackamores exactly like the one in the pic. The only thing you have to watch with a hackamore is not pulling back on it too hard for too long. You can cut off a horses air and that is BAD!!! (obviously!!!!
) With hackamores you have to pull back briefly and release. If the horse doesn't stop you just do it again until you get the result you want. It's just a matter of always pulling and releasing straight away.
As for bolting while you had a hackamore on her. . . . You would have the same amount if not more control over her. A hackamore puts pressure over a horses nose which is a very sensetive part of their body. They respond to the pressure once they learn that it will not cut off their air if they stop immediatly. If she does bolt and continuous pulling and relaesing does not slow her then you would either have to try and turn her in a tight circle or if you feel you or your horse are in extreme danger then you could pull steadily back until she responds. You must be careful doing this for obvious reasons but once she feels her air being even slightly restricted and not released she will know she must stop to reduce the pressure on her nose. It should just be instinctual.
The best way to avoid having to do that is to train her to stop for verbal commands as well as the slightest pressure on her nose. That way you have more options to stop her rather than resorting to force. :)