Do you do any ground work before you ride? This can sometimes give you a huge indication of what state of mind the horse is in before you get on, and that in itself can keep you out of danger, by keeping you out of the saddle for a little while in order to gain his attention back. If a horse is nervous or anzty before you even get on, then that is how he is going to be when you get on, and his reactions could be even more exaggerated.
You might want to do some longing, and desensitization exercises with him, using flags, and ropes so he will calm down, relax, and stay intune with you from the ground up. Being you and him are new to each other, as someone who trains horses 'for a living' now, I can not stress enough how important ground work is, especially when you are new.
You may also want to find a personal trainer who can help you learn and remain calm through situations like the bolting; even if you don't realize it, you may be contributing to the problem by subconsciously anticipating the bolt, which is why he got continually worse through out the ride; having a trainer who can help you work on your 'stuff' can greatly help your horse, especially if, when you tried him out before you bought him, and he was fine.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."