While I'm no expert on shooting off horseback, we are training our horses so we can bowhunt from them.
Similar to what was posted, we started by tying them up behind us as we shot at a target at 40 yards, the logic being it's enough flight time so the horse can differentiate between the shot and the impact. Being behind us, the noises are a little less sharp than if they were beside us.
Then, we moved them beside us, about 20 feet from us, again, moderating the noise factors until they got accustomed to it.
Then, three feet away...
Honey's horse is doing fine, mine buggers every time.
Then, hunting season rolled around, the horses weren't ready, so we hunted on foot.
We'll start back up again later this month, as spring breaks and temps get warm enough to do the training properly.
I RIDE, THEREFORE I AM
COWBOY UP OR GO CRY IN THE TRUCK