There is a big difference to when a horse bolts and when it runs away and the rider doesn't know how to apply the brakes.
...I learned that swinging their head from side to side, not see sawing but swinging them out of their stride stopped them from reaching over drive.
When I went into racing I had difficulty in holding a couple of the horses, one was notorious for hooking off and dropping his rider, when he tried to go on the down slope, I reverted back to the swinging off balance...
Stopping a horse that is hooking off is generally not difficult like many things, it is a knack.
I kind of like the worm trails.
I have been writing in my journal about my horse that has learned to evade being swung out of her stride when she wants to go fast. It's a strategy that has worked well for me on strong horses too, but situations happen and now we're trying to figure out how to go beyond when a horse has learned to evade it.
BSMS, situationally if the horse is already bolting I agree about staying on. But sometimes it can be safer to bail if a horse pulls up for a second. That's why I practice my swift dismounts and can leap off a horse in a second. Once at a poker ride a mule bolted off with a pack full of empty beer bottles. If you can imagine the racket of a screeching mule plus the swooshing of a pack full of clanking bottles...our horses were terrified. The mule fixated on my horse as the solution and my horse ran and the mule chased. We were running super fast around a circle, my horse running for her life and the mule chasing after. I was just hanging on. Finally the mule took a breath and my horse braked for a split second to see if she could run another direction, and I was off. The second my feet hit the ground I grabbed my horse's reins, stopped her, the mule pulled up short behind us and the mule's owner grabbed the mule.
I still call it bolting with those special horses...like Booker who took the bit in his teeth. He'd do it gleefully but take all control and would not slow his gallop down steep ridges, over terrain full of downed trees, flat out toward slick pavement. You find yourself calculating the odds of the horse breaking legs, which way he'll topple or will he slide straight when we hit the pavement, etc.
As far as the technique...sometimes it is different for different horses. We all knew how to prevent this. If we were going to gallop, whoever rode Booker had to "check his brain" and make sure the rider had the bit before we took off. If you did this, he'd willingly comply and he was super easy to rate. If you forgot, that was your problem. He'd never give the bit back until he was ready. When a horse has the bit, you can't do anything. Physically you can't break it loose, I've tried and others have tried. I always thought this was an expression until I met a horse that could grab the bit. You can't control speed or direction.
As far as collection, if people want to disregard the studies that show the weight transfer onto the hind legs during collection is very slight and that the force on the front legs increases, and if they want to disregard that when the spine is taken out of the horse and manipulated the amount of bend it produces is very small, then that's up to them. I am the type of person that will believe a study over a feeling.
Collection requires muscle tension, strength, and is not better for a horse or easier on a horse's body. I believe if we could accept it as a style of riding rather than the
method to create horses that move "better," or use their bodies "best," it would help the less informed.
The idea of round is why a woman I know pulls her horse's head behind the vertical so he can't see on trail rides, which makes him nervous. "Arabs come out of the womb with their head behind the vertical" she told me once. "Haven't you ever been to Arab shows?" Um...yes....
The idea of round is why another woman I know puts draw reins on her Quarter Horse and canters him around and around the arena on his forehand. She told me "If he can't get his neck rounded over he can't use his back properly and get under himself."
The idea of round is why another rider I know has not progressed beyond the walk in her dressage lessons after six months. Every time she goes faster the horse lifts his neck and pushes his nose out, so they go back to working on "accepting the bit" at the walk. All of these beginner level riders (and their instructors) have bought into the idea that a rounded over looking neck and back is the way horses must move.
If they enjoy doing this, it's fine. But please don't try to sell this as a universal principle for horses and riders to follow. Which I've seen as people in disciplines from reining to hunter to pleasure to even endurance have bought into the idea that horses need to "round up" in order to carry themselves properly. I'd like people to understand this look has an aesthetic appeal but is not a physiological necessity. I'd also like the style to become less fashionable so we could appreciate the different anatomy horses are born with rather than trying to make them all look like baroque horses.