When I've had horse bolt, I have either pulled head around to knee, and circled, or depending on the area bolt has occurred, urged them on. Horse realizes "hey, she wants me to go faster, well I don't want to!" and slows up and comes back to hands.
As for rearing horse, I bring weight forwards, and drive horse forwards with legs. BUT if horse is wanting to develop a habit of getting light in front end, so as to scare off rider, I either take hand and pop between ears, or have also used egg, or whip handle to thump them there. Whiskey bottle with warm water works too, but then have mess to clean up. The egg, running down their face, gives them something to think about, the tap/pop does too. But it has to be done with a horse that is developing the "I don't want to so I will rear" rather than a confirmed rearer that has gotten past 45 degree angle.
When horse is almost straight up? Too late for much of anything then. Problem needs to be fixed before that point.
Bucking is thwarted by keeping head up, and moving forwards, or anything that can be done to redirect horse's mind.
Bailing off is case by case. Sometimes you just come off, sometimes you have a choice to push free, or roll.
And while I agree there can be holes in training to be fixed? Horses are living creatures, and even the best trained horse can decide "I don't want to" and all the training in the world is not going to help then, if horse really puts mind to it. They are not machines, they think and may do things they know not to do, simply because they can.
Horses make me a better person.