I'm glad to hear that you're going to be ok. When first backing a horse IMO it should always be done in an enclosed area. When we start horses, after all the groundwork is done, we always back in the roundpen. Then, after several non evental rides, (at the walk) we go to the arena and ride there. (at a walk) Once we know that the horse has the walk, turn and whoa down, then they are moved up to a trot. We also work with other horses in the arena. We will do things like walk past them, then trot up from behind them and once they are comfortable with that, another horse is loped around them. They will not be moved up to a trot or lope until they are comfortable with all of this. The first trot and lope is done in the round pen also. You want them to get used to the movement with a rider on them, without giving them the room to panic and all out run and buck. Sure, they can buck and throw you in a roundpen or arena, but If you've done all of your homework and gone slowly with them, the likeliness of it happening decreases.
After they can walk, trot, and lope in the arena, they are ponied out on the trail a few times. It is always with calm, experienced horses and experienced riders. After ponying, then they can go out on the trails with the same calm, experienced horses.
IMO (and I'm not saying you did this) too many people push their horses to go to fast in their training. (by fast, I don't mean speed, I mean pushing their abilities, both mentally and physically.) The slower the better.