Yes, but you have to flesh out your fictional world around it.

Lets assume your world has bear cavalry. That is a - fictional - fact (sic).

Lets also assume that this has been so for some centuries. There is a tradition of bear cavalry, and the kinks have already been solved.

Your bears are not only domesticated, but also selective bred from wild bear stock for some time now. They are to wild bears what dogs are to wolves now.

So, from the answers of my esteemed worldbuilders here, these are the characteristics your bears have been selected for:

1. Not eating their handlers.
2. More Stamina on extended sprints.
3. Profile. The war bears would have a better rider-supporting profile. Horses and camels allow the rider's legs to stay relatively stable, and an elephant is rigid enough to allow a howdaw. The bears need to bear a saddle of sorts. Give some thought to the design of this saddle. After all, if it is a bear cavalry, it is assumed the rider fights too, and not just steers the bear.
4. Diet. fgysin suggests eating the fallen enemies. I think that if this is done, it should be ingrained into the culture, into a sort of ritualistic proceeding of cleaning up the battlefield. Just allowing the bears to ravage the fallen is bad, since making the bears eat people can teach them how delicious they are. see #1.
5. Diet yet again. Maybe the bear cavalry works in your world because of some rare protein-rich plant that can be grown to feed the bears. This plant might be mild poisonous to humans, but bears can eat them without any issues.

Yes, but you have to flesh out your fictional world around it.

Lets assume your world has bear cavalry. That is a - fictional - fact (sic).

Lets also assume that this has been so for some centuries. There is a tradition of bear cavalry, and the kinks have already been solved.

Your bears are not only domesticated, but also selective bred from wild bear stock for some time now. They are to wild bears what dogs are to wolves now.

So, from the answers of my esteemed worldbuilders here, these are the characteristics your bears have been selected for:

1. Not eating their handlers.
2. More Stamina on extended sprints.
3. Profile. The war bears would have a better rider-supporting profile. Horses and camels allow the rider's legs to stay relatively stable, and an elephant is rigid enough to allow a howdaw. The bears need to bear a saddle of sorts. Give some thought to the design of this saddle. After all, if it is a bear cavalry, it is assumed the rider fights too, and not just steers the bear.
4. Diet. fgysin suggests eating the fallen enemies. I think that if this is done, it should be ingrained into the culture, into a sort of ritualistic proceeding of cleaning up the battlefield. Just allowing the bears to ravage the fallen is bad, since making the bears eat people can teach them how delicious they are. see #1.
5. Diet yet again. Maybe the bear cavalry works in your world because of some rare protein-rich plant that can be grown to feed the bears. This plant might be mild poisonous to humans, but bears can eat them without any issues.