The Bear appears The Big Brag and The Rabbit, The Bear and the Zinniga Zanniga.
In the Big Brag, he overhears the Rabbit talking about how he is the best of the beast in all the land so he and the rabbit argue over who is better than who, after he saw the rabbit's talent on how well he could hear by hearing a fly on a mountain coughing, he knew that his ears couldn't do that but he told the rabbit he had a good sense of smell so he sniffed and snaffed smelling and smelling and he explains to the rabbit he smelled something way past the fly on the mountain.
He smelled past many great mountains beyond 600 miles past the edge of a pond where there is a small farm that has a tree that also has a nest on one of its branches where there are two small humming bird eggs at rest where there is a mother humming bird. He proclaims that his nose is so wonderfully strong and so good that he smelled without fail that the egg on the left was a little bit stale.
He then proclaims that he is better than the rabbit but a Worm came up from the ground hearing enough about the rabbit and the bear arguing about who is better, so he proclaims that he could see many miles around the world and she shows them how he can do it and as the worm told them how far he has seen across the world he points it back to where he began and proclaims he's seen two biggest fools ever to be none other than the rabbit and the bear who argue about who is better. The bear and the Rabbit looked at each other clueless as the worm dived back into the ground.