Try asking him to canter and then bring him back after one or two strides, then gradually increase this all the while keeping calm and relaxed.
Do this until you canter canter half a circle and then do it the other way. Keep changing things up so that he doesn't get bored.
Diddo on what Lucy said. I used to have a horse that would bolt and I would get really nervous before cantering. I just needed to stay calm and think clearly on how to stop him and how to prevent him from bolting. I would freeze and he would take advantage of me because he knew my weaknesses in riding. Sometimes singing your favorite song helps. Also, keep him in the bit or distracted and be precise on what you are asking him. Trust him, but really pay attention to him. He's watching every move you make, so you need to watch every move he makes and know the signs and stop him before he bolts.
I personally would lunge him first. Not to get him tired, but to see what he does during upward transitions himself, and it'll help get a bit of his craziness out. Maybe try picking up the canter, cantering a 3 strides, then halt immediately. This won't give him enough time to do anything, and it'll keep his focus 100% on you. I would highly recommend lunging him for a while just so you have a better piece of mind. I hope this helps. Happy riding!
I'd work on canter transitions on a circle. If he speeds up without you asking, bring him back to trot. If he doesn't respond and feels like he's going to bolt, do very sharp turns and work on teaching him a one rein stop. If they're turning in a very tight circle, they can't go anywhere and will soon find it easiest to stop rather than bolt.
I'd also recommend doing lots of groundwork and lunging to get him focused on you before rides. Ensure he respects you and your cues, make sure he knows to slow when you ask. If he doesn't, speed him up and make him work harder. Make being relaxed a reward for him.
Although it can be nerving, especially when you've got a hot horse on your hands, it's best to stay calm by breathing, relaxing your shoulders and to always remember to give your horse clear cues. If you're nervous and accidentally telling him to go one way, then the other, etc he'll become confused and will bolt as a way to escape the pressure.
Hope this helps!