While there is room required for the one rein stop, there is another similar technique that may have prevented your need to bail. It's called the pulley rein. You sit square, plant your right hand and rein against the horse's neck in a fist so it doesn't go anywhere and use the left rein to slow him down little by little in short bursts by pulling it away from his neck just enough to get a little flexion each gallop stride. I wish I could find video of it since it's a bit hard to describe. This move can be done in a straight line. Just this past week I watched a jockey use it after a race on a horse going at least 35mph. He stopped to horse on a straight line. It was very impressive.
I can't help you with the bit question since my horse I have never been on a horse who is heavy in the mouth.
Yes, this is actually a very common move with jockeys, as it's too much if a risk to do a one-rein with them. The basic idea, is that with some horses (expecially hard-mouthed ones/hot horses) by just hauling back on the reins, they are able to grab the bit/ lock their jaws against the bit which is basically them driving all pain from their mind. If you do a tug & release/ pulley-system, then it's not a constant stimulus & the horse can't numb themselves to it.
You can try a hackamore if you'd like. My friend's bf had a mare who was horrible for bolting (she'd do it on trails, going downhill!
) They put her in a hackamore & it worked wonders for her
. Make sure you have a chin strap, though.
For a horse like that, i wouldnt use a bitless bridle, as i've found they're no good at slowing a horse down if they dont want to be slowed. They are, however, very affective at turning.