I have no first hand experience with bear encounters, but have done a bit of reading on the subject. (Not the same, I know!!)
There has not been a Documented case of bears attacking people on horseback. (At least not at time of publishing, maybe 6 yrs ago.)
So #1, don't fall off your horse, lol.
The most dangerous bear is a sow with cubs, especially if you have inadverdantly gotten in between them! So the general rule of hiking (and riding, I guess) is that you Want the bear to know you are coming... so make noise. Bells, sing, a whistle blown every so often. They will move off right away.
If you encounter a mama bear, act submissive and back away. Make sure you are not blocking Her escape route. If she attacks, it is my understanding that this is when you play dead, she will leave with her cubs when the threat is gone.
If you encounter a predatory BLACK bear (wants to eat you), make yourself big, loud aggressive. If it charges, hold your ground, may be a bluff charge. If it attacks, fight back with all you got.
Mama grizzly, same as black bear, submissive, no eye contact, slow retreat, play dead.
Predatory Grizzly.... you're screwed.
Anyone, please correct me if I made any errors!