At the OP - we have a lot of black bears in my area too. Our Fish and Game enforcement have also quit relocating them because there just aren’t places to take them. Like your state, they will only euthanize a bear that has become a threat.
Best advice I have is make sure there are no garbage containers or bird feeders where the bears can get to them (it’s an attractant). Also, if you have blackberries or other wild fruit that might attract the bears, make sure to clear that out.
Lastly, if your pasture area isn’t too huge, you could regularly spray bear spray around the outside of the fencing to help discourage their appearances.
If it were my horse and he needed to be conditioned to accept the occasional presence of bears that are not threatening, I would probably look for a bear skin or something that I could use to get him accustomed to the scent of bears. Then slowly increasing his time with that scent until finally, putting him out where he can see them and when one arrives try to keep him as calm as possible until he gets past it.
Based on other posts here, it sounds as though it can be done. I don’t envy your situation. Good luck.