Perhaps take a hint from the Greeks, and the Centaur. It was a human torso on a horse, not a bear or lion. There is just something about the scale of a human and horse that seems to work. The human is big enough to control the horse, without appearing to overpower it.
So your bear or lion should be about the size of a horse.
It would have enough bulk to be intimidating, and large enough to allow a good solid, sturdy mounting platform, or saddle. The scale has to be such that the beast has enough strength and flexibility to carry the rider, and still has plenty left over for combat. A smaller animal would, I posit, spend more energy on carrying the rider and adjusting to the rider's position, than in providing any support in combat. Also, if the human were too big in proportion to the animal, weight distribution would be problematic. The center of gravity of the combo would be continuously shifting.
Elephants are actually too big for practical combat. They are too energy-intensive in terms of food. The feed/utility ratio is too high. Hannibal would have had to carry more in food for the elephants than they alone could carry, so they were a net negative as far as carrying supplies. An elephant eats about 400 pounds of food a day. There are far better uses for 400 pounds of food, even if you can source food locally.
