I will make it a point to be more vigilant whenever I go past this hedge. But how do I prepare for the event the horse might bolt/buck or shake his massive butt?
Bolting was discussed several times in I believe "Riding" or "Training" section. I'd suggest to do some search there. There are 2 approaches to stop the bolter and I remember for sure people posted videos on how to do it. You again want a good sit to be able to sit through the bolt, and yes, you can turn the bolter in circle in arena (harder on trail, because it may be too narrow).
P.S. Paying more attention to surroundings helps tremendously: sometime you already know what is coming and you are ready. The reason why I never ride with player/headset on (even though bunch of people do it): I want to hear what's coming. :)