A horse that is truly bolting is a horse that has completely panicked. If you read Watership Down, they talk about how rabbits go "tharn" - freeze, and lose all reason. True bolting is similar, except that the horse will run as fast as physically possible away from the source of its fear, not caring for anything or anyone that gets in the way.
If you're riding a horse and it bolts, it's likely to forget you're there and scrape you off on a tree branch (I've known horses to try that on purpose, but believe me, there's a difference). It may stumble, pitch you over its head, and then step on you as it keeps running. I once saw somebody almost get killed stepping in front of a bolting horse trying to stop it. The woman was at least 200 pounds. The horse didn't even slow down.
Fortunately, horses don't bolt very often! (Again, it's a very overused term). A good horseman knows to wait until its calmed down and not attempt to catch it unless it's running into a dangerous situation, such as a busy road. When I rode with cowboys they carried lassos - so that if a horse tried to run for a road, they could rope it and catch it that way. For that matter, it's dangerous to try and catch any horse that's moving at speed unless you're on another, preferably larger, horse.
The best thing to do is to shut all gates and let the horse run itself out - they stop eventually. If that doesn't work, pacing them on another horse and waiting for them to return to sanity, then gently turning them to a stop is also effective.
If you want your hero or heroine in real trouble on horseback, have something panic their horse...and you can have them end up on foot in the middle of the woods, or maybe still on horseback...in the next county. With a lame and upset horse.