I won't speak to bucking, since my horses aren't buckers.
If one has room to spiral down, that is fine.
But a pulley rein is basically a way to gain leverage in using two reins to stop, and the positioning used makes it harder for the horse to throw its head up or go way down. The problem I've had with it isn't in getting the horse to stop, but keeping the horse stopped. Still, a pulley rein stop followed by successive 180 deg turns as the horse starts to think about bolting again has worked for me - as has spiraling into a tighter circle until the horse slows.
When I tried steady pressure on Cowboy during his first ride with us a year ago, it didn't work too well. In a sense it did, since I didn't mind doing circles at a gallop until he realized I wasn't going to give in, and then he gave in and started responding to far less pressure:
Something I notice looking at this picture is that the angle of my pull left Cowboy's head only about 30 deg below horizontal. I'm beginning to think that getting the head at least 60 deg below the horizontal may be a big factor...
He hasn't repeated that act since that day (2 Dec 2011), and Mia hasn't bolted since then either, in the sense of a fear-based bolt. Mia has
taught me the meaning of "got the bit in her teeth" on a few rides outside the arena, when cantering near another horse brought out her inner Secretariat. She won't do it in an arena, but on a trail she's decided she was going to win by 30+ lengths.
With no room for a spiral, I've tried A) see-sawing (making very small zig-zags down the trail), B) rubbing her neck with my free hand while calling her name softly (I'm batting about 33% on trying that technique), or C) pull **** hard/pulley rein. C worked the best. The other day, I tried D) bumping on both reins hard. It actually worked quite well, but she wasn't nearly as excited so that wasn't a fair test.
We're doing remedial work on our stops in the arena now, and some on the trail. I asked our farrier. He said he once owned a horse who was great, but only AFTER he galloped 2 miles on his first ride of the day. He was riding bulls for fun back then, and thought it was fun to do the 2 mile bolt every morning...but I'm not 19, and have no desire to ride bulls! If anyone has any ideas or suggestions, I'm all ears - or all eyes, since this is the Internet. I continue to be a fan of having as many ideas as possible in your clue-bag in the hopes that at least one will work when your horse hits the fan
...or when she decides she is in the Belmont!