A few comments from someone who bought a horse on a whim 4 years ago, and then started to learn how to ride...
1 - Bolting. Although my horse was sold to me as being great for a beginner, 3 years later the trainer I hired concluded she had never been broken to ride. At all. So the trainer started her at the very beginning, on the theory that part of her fear was caused by having no idea what the normal cues meant. That plus desensitizing - which is NOT about creating a laundry list of things that are not scary - has done wonders for her.
But a big part of what was needed was for me to progress to a point as a rider where I don't freak if she bolts. For me, that meant taking lessons on other horses until I could stay calm at a gallop. Horses don't naturally bolt for a mile. They bolt for maybe 50 yards or so. When they keep galloping past that, there is a good chance that rider fear is causing them to stay scared.
Mia started professional training last November. Over the last few months, she has bolted a few times in a narrow wash. I just ride her until the wash is wider, then turn her and take her back thru the scary place. But to do that, I had to progress as a rider to where I could respond to a bolt with a sigh, followed by figuring out how to stop her.
That brings up #2: One rein stop.
The one rein stop is a learned training response. Like doing some gentle see-sawing on the reins, it only works if the horse is willing to listen to your inputs. It is possible to have the horse's head pulled 180 degrees and the horse still galloping out of control. Been there, done that. If you try breaking your horse's ribs with your legs - and I say that out of personal experience and am not saying you do that - then a one rein stop won't stop them.
3 - Confidence in you. What worked better for me than round penning was simply taking Mia out for walks. On a lead line. Like a dog. At first, we only made it 100 yards before she would panic. In time, we worked up to 3 miles. It is vastly easier to stay calm when you are on the ground. And from my limited experience with one horse, when your horse learns you know what you are doing, they are far more likely to listen when you are in the saddle. I'd guess about 50% of the confidence they get from being led carries over to when you are in the saddle.
4 - One thing worked extremely well in the round pen: getting her to calm down after getting excited. At first, if I pushed her to a gallop, she would then do 12-20 laps of the pen at a gallop while I just stood steady. With repetition, starting at a trot and then moving to a canter and finally a gallop, she learned that it was possible to calm down after getting excited. The trainer was supervising me, and she didn't think Mia was ready for more training until she could calm down from a gallop to a walk in about half a lap.
I don't know if any of that applies to you. It has been a long road with Mia, and we're now working on her learning to go out into the desert without any other horses. She is making good progress. I find I now constantly monitor her attitude, because a big part is learning to recognize when she is about to get scared, and backing her off before she goes bonkers. I've taken my time. A major part of every ride is convincing her that life outside the corral can be boring. Neck almost level (she's Arabian), ears forward, relaxed back - I want that to be a big part of every outing.
Also, I cheat. I use an Aussie-style saddle because it allows me to get my legs down and wrapped around her, while also being a deep & secure saddle. I can do that with some western saddles, but not all. 99% of the time, my Aussie saddle rides like my Bates English AP saddle, but it sure is good for those times when the horse hits the fan, so to speak. I've thought about getting her a barrel racing saddle - deep seat, designed for going fast. I don't care if it is my imagination. At 54, my body doesn't heal very fast. If some piece of equipment makes ME confident, then it will give HER confidence as well. I figure if you aren't cheating, you aren't trying....
Good luck! I know exactly how you feel!
Mia getting ready for a ride this summer:
Bits: I was using a D-ring snaffle here, and sometimes use a full cheek. She currently is using an eggbutt copper snaffle with curb strap attached. I did come close to pulling a loose ring snaffle thru her mouth once. I also see nothing wrong with using a harsher bit, if you have good hands and are working your way down. I've concluded that the switching of bits is endless, so Mia has her quick change bridle on...allows me to change bits on a whim. But if I'm honest, I'm not even sure she cares what bit is in her mouth...