It is known that when a horse bolts or won't listen to your signals to stop, he is running away from the bit, it hurts to get pulled, and this is the only way a horse can tell you, so he takes off....
But don't worry there are solutions to this, other than putting harsher bits on them.
We start at the begining, Does the horse respect your space, is he pushy, unrespectful are you in control on the ground or is he. If not gain control, find someone who knows about horses, get them to re-educate the horse, and teach you how to do it...most of all listen to them.
Lunging may help, walking first if he is ok with that, then continue in the trot and so on. If you don't have control in one of these gaits then go back to the one you have control of, keep repeating this until you have respect on the ground or you will get hurt.......... then with a sirsingle use side reins, tighten as you need to, this gives the horse a chance to have the bit in his mouth without being tugged all the time, may help to get a softer mouth in the end.
There is so much more, that is why I suggest you find someone local.
If I can help any more please leave me a message.