My horse wasn't inclined to bolt, but was terrified
of bikes when he was green. What fixed it was asking riders for their
cooperation in riding away and allowing me to "chase" them for a
while. Like Elizabeth inadvertantly taught her horse with
hubby. This seems to give a horse confidence and makes him think they are
running from him. This is the nature that cowboys reinforce for working
cows. We did this with both mountain bikers and dirt bikers on the trails,
and after a couple times with each, he was very comfortable with
them.
As for the bolting. To some extent I believe
it can be improved upon by establishing leadership. A horse needs a leader
to feel protected. Otherwise, in their mind, they are a
more vulnerable prey animal. If this is established (through basic
respect, discipline, ground control) and solid, it will be much better.
Some horses are more spooky than others, and all horses will spook, but not all
horses will bolt afterwards. If they feel that the person on their back
will protect them, there is less need to run away.
I know this isn't a 100% guaranteed fix, but I
would start here. :)