Let me start by saying I have never been bucked, thrown, or even fallen off a horse. I actually tried to fall off Hoover, but always caught myself. I've never had an injury beyond a few scrapes. I love horses, but have always had a terrible fear when first mounting, and for a while of falling or having the horse take off with me.
As to the first, I haven't found a solution. I just suck it up and get on. I guess it only makes sense, as it's a particularly vulnerable time for a rider...one foot in the air, only partial control of the reins, etc.
The second Hoover fixed for me, in an odd way. We were having an argument about turning, and he gave up and fell over. On me. We both got scraped up...my elbow and his nose, and it winded me horribly. He came over and started pulling my shirt he was so worried. After a half an hour talking to my instructor to understand why this had happened, I got back on him. While I was scared at first, I fixed the problem (which had been my mistake), proved that Hoover would wait for me if I did fall, and learned falling didn't hurt all that badly.
The third is from an incident. I was riding with a friend, and the barn she was at had given me a hot mare, which I didn't know. Her owner ran her the trail we were riding. She fought me and fought me to go faster until we reached a massive downhill...and she took off. I had her chin in her chest and she didn't care. She took a three foot high tree trunk, charged across the creek in the valley, and started up the other hill weaving through the trees. I finally got her stopped, and nearly fell out of the saddle, clinging to a tree and bawling. In retrospect, she had beautiful form and it felt like flying, but at the time I was convinced I was going to die. Ever since this, when riding a horse downhill, I had a moment of crushing fear that this will happen again, even with Hoover, even with our sweetest, most level-headed lesson horse, Pappy. I have to admit, it has gotten better with time and knowledge of the horse I'm riding, but it comes right back if the trail or horse is unfamiliar.
The other thing that my trainer has done for me is forcing me to ride spooks, which has really built my confidence. I can specifically remember riding Duke with her riding Drift...Drift is losing sight in one eye, and spooked badly. I was suddenly facing the other direction with Duke tearing across the paddock, and me crunched up with a death grip on the horn. And I suddenly realized...how is Duke supposed to know I want him to stop? So I did as I had been trained...dug my feet into the stirrups and leaned back, slowing pulling him up.
I guess a lot of my fear is situations I don't know how to react to, and making them worse instead of better. Knowing how handle them seems to be the key to me dealing with the fear better.
"Sit tall in the saddle, hold your head up high. Keep your eyes fixed where the trail meets the sky. And live like you ain't afraid to die...don't be scared, jut enjoy the ride." - Chris LeDoux