There is a big difference between a “run off”, and a “bolter”. A run off just picks up speed, but you are perfectly safe, and he will slow down at the appropriate time. You can “ride him as fast as he can run”. It’s not good for him, he is not supposed to be going that fast, increases risk of injury to him. But you try to keep things down to a dull roar as much as you can, sit still and keep a hold on him, and wait for him to slow down.
A bolter is a different situation, not only are you “at speed”, but you have no steering either. A true bolter is very dangerous, for you, for the horse, and for others on the track. Because he is “running blind”. This is often a horse who is in a panic with his objection to training, his brain is turned off, “the lights are on, but no one is home”. Don’t ride a bolter. He will run into stuff, fences, other horses, people.
OP, make sure that you are working for a quality trainer. There are trainers who are “famous” for starting riders, exercise riders and jockeys, and doing it well. They make good decisions for you, do NOT put you on horses that are not suitable mounts for you, and impart a variety of information about successfully galloping race horses that is important to your growth as a rider. They bring on riders just like they bring on quality horses, with a long term goal of teaching you what you need to know to be successful as riders. Make SURE that this is the type of trainer you are working for. There are other types of trainers, often those who have never been a rider themselves, who don’t have a clue, and don’t have YOUR best interest at heart. Don’t ride for trainers like this. It’s hard when you are just starting out, don’t know everyone at your track or in your area. But ask around, and be careful. It’s real easy to get hurt if you are working for the wrong person, and green. I did this myself when young, ended up with a broken neck… got on a young horse who was supposed to be broke, but wasn’t. Rode more horses later that morning too, after that one. Felt bad. Went in for xrays two days later, found the break, people talking to be about the possibility of being in a wheelchair for the rest of my life (which didn’t happen). The trainer gave me the $5 for the ride when I went back to visit wearing my neckbrace a few weeks later. I learned something that day… to look after myself, and to only work for trainers who have a clue, and horses who were broke. I actually always preferred to only ride MY OWN horses (who may or may not be kinky, but at least they were MINE). No one else would ride the horse that broke my neck after that at the training center we were at. She was shipped to the track, where she also dumped one of the big boys, who got up and beat her up. She went on to a successful race career, eventually, but was not a nice horse. It turned out that where she was sent to be “broke”, she bucked everyone off daily, and was not broke. Then sent to the training center, where I got on her. Trust no one. Good luck.