Wow, that sounds EXACTLY like what my mare used to do. Except there was only about a 40% chance we'd go over the jump. She liked to run out, slam on the breaks, or 'bunny-hop'.

This worked well for my horse, so try it out if you like. First, get a friend/trainer to help you from the ground. Set out your jumps, but take them down to ground poles. Make horse trot and canter over the 'course' a few times, making sure she's totally calm and maybe a little bored. Then have your friend put the jumps up to the lowest setting possible. Trot and canter over this course until it's boring. Now raise the jumps one hole. Go over the course. Repeat until you're jumping the height you want. Generally the gradual increase in height doesn't excite the horse nearly as much as starting out at 2' or so.

My horse's problem was caused by her not knowing exactly where the jump was and not knowing where to put her feet. By going over the course as ground poles and low low jumps we built up hr confidence and she was much more willing and calmer when the fences got higher. I got her up to 3'3" using this method.