I have certainly seen horses bolt in curbs, particularly as a kid when there were little girls on half trained “western” horses “bombing around” everywhere.
I have also as an adult seen very effective use of one reined stop or pulley rein to halt horses ridden English.
Basically whatever bit, if you just haul straight back the horse can lean into it and bolt. A snaffle gives you much more ability to circle or use one rein.
Interestingly as a teen I thought of my long shanked mechanical hackamore as my bit with the most “stopping power.”
I dug it out of the basement and am using it for trail riding with my current horse. And honestly I feel more in control with a snaffle because I know that I can do more to stop, to circle, and to rebalance.
Also 100 % yes to doing as much exposure to obstacles and stimulus as possible. I like to work with obstacles by putting myself between the horse and the thing, and walking around it at the edge of the horse’s comfort zone until that comfort zone lets us get close and close to the thing, and we just march over the tarp or up on the circus box or whatever. It isn’t just about the specific obstacle but about developing a protocol for approaching new things so both you and the horse know what to do and the horse knows he can trust you not to overload him with new things.
Might be useful to have someone ride a bike around you in the parking lot, walk past you with a stroller or an umbrella, playing a guitar (really) anything that might turn up on your trail system.
I expect as a roper he is more used to stimuli than maybe a barrel racer that is kept penned up to just sprint full blast on competition day. I also think that a roper might be a more confident horse, in that he has to chase after cattle. If he has been used for ranch work he has seen his share of border collies, tarps, tractors, and other horses running loose.
Also probably good to practice whatever speed work he knows in the arena, so if he does a good slide or spin, you know about it and can sit it.
All that said, I still think my biggest safety tip for riding is: choose your riding buddies wisely. Don’t go out with the hotrodders, don’t go out with people who aren’t in control of their horses, and don’t go out with anyone who wants to push you past your comfort zone or thinks racing on the trails is a great idea. You are much safer alone (especially with a cell phone) than you are riding with high-risk riders. Take it at your own speed.