Dungeons and Dragons is a fantasy game filled with fantasy monsters, and normal animals like bears may seem out-of-place as antagonists and challenging foes. But sometimes we forget (or younger folks may not be familiar with) the rich literary tradition that is the foundation of the "stuff" in D&D...it's a lot less fantastic than one might think.
Tigers, bears, crocodiles, and snakes (constricting and poisonous, both), these are the "monsters" many sword & sorcery heroes faced when not fighting their main enemy: other humans.
I think we often lose sight of this...it's easy to draw a map and stock room after room with "fantasy monsters" - orcs and bugbears and dopplegangers and carrion crawlers and whatnot - and while we might write an adventure so that it makes sense from the POV of "Gygaxian Ecology," it may be so fantastic as to be alien to our "real" adventurous history. When Lewis & Clark opened the passage to the west, a grizzly bear was a pretty serious threat, as their own accounts tell...and they were traveling in a large party and armed with modern firearms. Sometimes we take for granted the power and majesty (and threat!) of real life nature.
Yes, S&S heroes like Conan fought the occasional fantastic creature...the frost giant daughter's brothers or the naga-like man-snake. But most of his foes were extremely natural. Even Tolkien, "high fantasy" that it is, isn't filled with supernatural encounters/combats. What are goblins/orcs but "twisted elves," and what are elves but more sophisticated men? Take away all the battles with orcs and how many real "monsters" are encountered in The Lord of the Rings? A troll, some undead, a giant spider, a balrog. And the usual reaction of the heroes to ALL these threats is "run away! run away!"
A very different set of heroics compared to that of your average D&D party.
So give nature...and natural "monsters"...their just and well-earned due. A mountain lion or panther or wild boar or (God knows) BEAR can be plenty challenging to an adventuring party...especially low-level ones. True, they might not be found in your average "dungeon" or tomb/haunted crypt (animals are notoriously wary of the supernatural) but getting to and from the adventuring site can be fraught with peril without involving anything "mythical" or "fantastic" at all.
Just think about it, okay?
Now, if you'll excuse me, I have to write something up about demons and giant frogs and assorted craziness.