Relax! When I first started cantering I felt the same way you did. Long story short I had seen my mom fall off, so naturally I was afraid to start cantering. My trainer was persistent and we eventually started on the lunge line. It was actually really fun! I learned that cantering is just another gait. Now I'm working on getting over my nerves about jumping 3'!
Anyway, are you working with a trainer? If so, you should talk to him/her about your fears. They can help you get over them by taking it slow. Maybe you need to build up your confidence more at the walk and trot on different horses. It's okay to take your time. You don't need to rush into anything.
Being on a runaway is pretty scary! Just remember your one-rein stop. However, in some situations if your horse is really frightened you need to just let him run a few strides then circle him at the canter or trot. Just like falling off, you need to chalk it up to experience. Now next time you will already know what a bolting horse feels like, so you will be able to act accordingly or try to keep their attention on you more.
As you already know horses are animals and are unpredictable. You are probably going to be on more horses that shy and buck and bolt. You just need to be prepared and stay calm. You could fall off your horse at a walk. Like I said, cantering is just another gait and you will have so much fun once you give it a chance!
Best of Luck! Tell me how it goes!