While you may consider yourself an experienced rider, the fact that you mentioned you want a horse that doesn't bolt on you? Makes me think you might not have enough horse experience.
All horses have the potential to bolt, if they sense the rider does not know what they are doing. Much of working, riding and handling of horses comes from knowing how to handle them, and not letting them get away with anything.
If you are taking lessons, your instructor will have the best sense of what type of horse you are suited for.
Horses make me a better person.