...I'm not familiar with the pulley stop but upon watching the video will definitely stick with the ORS. The problem with pulling back on both reins is that the horse can take the bit and bolt off. You can not overpower a horse and make it stop by pulling on both reins even with that little bit of leverage I would not feel safe trying the pulley stop besides the fact of how complicated it is. ...
A pulley stop does work well. When Mia was convinced she was Secretariat reborn and galloping without a thought of slowing, it brought her to a stop. It will not make a horse bolt.
A one rein stop is a technique, but it requires a lot of training too. Spiraling a horse to slow it down is not a one rein stop, although it is a very good technique if you have room. Where I live, there is almost never enough room to spiral a horse to slow it down.
There is no one answer, only a variety to things you can toss into your clue bag for when the horse hits the fan.
...Also if she is a bolter then a harsher bit will not solve the problem. It will only mask the problem. Too often people use quick fixes instead of actual training. I think switching bits is a pointless idea and maybe you should switch trainers because what I hear is someone who can't follow through and will use quick fixes even if it makes things worse in the long run. Instead of a harsher bit she should be properly preparing you and your horse by exposing her to trail situations and teaching her to use her thinking side instead of her reactive side...
A bolter can be controlled using a simple snaffle, provided you deal with the bolt as it is starting to happen. If you wait until the horse is racing at full speed, head extended, snaffle bit resting against its molars...then you're screwed. A pulley stop MAY still save you, or a ORS if your horse is trained for it, or a spiral if you have room - which is why having a LOT of tricks is a good idea.
Using other types of bits isn't hiding anything, but giving you options for when a snaffle has no impact on a horse. A snaffle bit works, when it works, with pressure inside the horse's mouth. If the horse extends its head and clenches its teeth, then a snaffle will have almost no impact on the horse. It just goes against the molars and the horse ignores it - hence the term, 'bit in his teeth'.
A curb bit has some mouth pressure, but also applies pressure to the poll, and can be used to leverage the head to a position that encourages a horse to slow (more vertical). Applying pressure outside
the mouth is a good alternative to brute forcing the bit inside
My mare also seems to respond well (instinctively) to a gag/elevator bit. She understands pressure on the poll. If she is calm
, she'll stop off of seat alone. But she isn't always calm.
Learning to read your horse and respond appropriately is an excellent idea. It is critical to good riding. One suggestion for the OP would be to lead your horse on a lead rope out of the arena and however far she is OK with. When she starts getting tense, try for one more step, then let it be YOUR idea to turn around. That will give your horse confidence in you, and will help you learn to read your horse. Mia and I started at 100 yards, and worked up to several miles.
With Mia, if she is getting tense about something ahead, backing her a couple of steps is all it takes for her to calm down a lot. If need be, I can back her a few more steps and she'll lower her head and relax. Not all horses act that way, but it is something I discovered about her from taking her for walks on a lead rope.