Mavis, ever ride that amusement park ride called the scrambler? The one where spokes of 3 cars each spin around as the whole thing revolves in one big circle? That motion is kind of what your body should do when a horse suddenly moves from under your center of gravity. Your lower body stays in the chair, while your upper body stays soft and goes with the flow. I know it doesn't help with what already happened, but maybe the visual will show you what you're aiming for as far as riding out a spook.
You just have to see your distance...you don't have to like it.