I can't help thinking that when folks are talking about "bolting" here they're talking a different language.
You can't and won't ever stop a genuine bolt from happening.
What you have to do is once the horse has bolted, hope (or try) to get the horse to "switch back" quicker and recover its composure when its being ridden. When its bolting its in a full fright and flight mode and if you're lucky it's looking after itself - its not at all concerned about anything else. As a rider all you have to do is sit on and try to get it to listen to you and switch back its attention on you and to steer it to safety if at all possible.
Half halting, turning in circles and one rein stops (which in effect just disengage the hind quarters and turn the horse's head) can all be helpful to put the horse off balance and get it to concentrate on something else rather than the true flight and fright bolt.
But don't go thinking that you can stop a true bolt.
I think what is most often being described is a situation where the horse has mistaken the rider's intent or got over-excited and decided to run on faster than wanted. And perhaps even grabbed or taken hold and leant on the bit in order to so do.
A horse that transitions from canter (or walk come to that) to a gallop and is staying in the likes of arena confines and going round in circles is either evading deliberately because its objecting to what is being asked of it, or else its mistaken the intent of the rider.
That's not a bolt though.
If it was a bolt, you'd have been through or over the arena!
If a horse takes hold of the bit and tanks off with you frequently then you really need to take a more holistic approach and review a whole set of circumstances and as described earlier. It's not "emergency strategy" that's needed. It's a management strategy.
It would have to be a dire situation for me to bale out and such that a horse had totally lost it's mind and wasn't looking after itself and was heading to leap over a cliff or off a mountain top for me to bale out.
Its falling and coming off that hurts
IF a horse is proper bolting (not a few scuttling strides away) regularly and at comparatively silly things e.g. A car that backfires, a tarpaulin that flaps, a person with an umbrella, then its a training issue without doubt. If a horse bolts because some idiot did something really dangerous and risky, then in my mind, that's a sensible horse just being a horse. The mark of whether its a good and well trained horse and what your relationship with it is like is how quickly you can get its attention and trust back on you and get it calmed down.
It always concerns me when someone asks how to manage a horse that is bolting or breaking out of canter or becoming uncontrollable and yet they're supposedly routinely riding out and sometimes even competing or exercising such horses. IMO the fact that someone's asking anonymous folks on a forum means they're not ready for such activity and need more lessons and practical guidance from an instructor.
There's really only one way and that is sit tight in order to help him maintain his balance and ask him to trust you and break down the flight fright instinct by just riding and asking using your seat and hands quietly.
If you grip and try to pull he'll get worse and no-one has the strength to stop a pony, let alone a horse if he gets strong and excited and determined when you canter in the open.
Rearing: Grip firmily with the knees and weight well forward so your body stays upright in spite of the back ward tilt and it it's VERY high, then arms round the neck if need be. Relax the rein totally.... IF you need something to hold on to then by all means grab the mane if you don't have a neck strap but ensure it's not going to have you too far back. If you happen to tip backwards and try to save yourself with the rein then you will likely over balance the horse and it may fall on top of you. Pulling the head to one side might help because he can twist in the air to land on forefeet. IF the horse goes well up then get your feet out of the stirrups so that as you start to slide you land on your feet.
As you feel a horse about to rear, quickly urge forward with most active leg aids and a totally relaxed rein... he can't go forward and up at the same time!