Here are some whose lyrics have already been posted at Mudcat:

(The Dance of) The Grizzly Bear
Bear
Biff, the Friendly Purple Bear
Cumberland Mountain Bear Chase
Dancing Bear
Eaten by Bears
Elmer and the Bear
Grizzly Bear
Grizzly Bear
Larry the Polar Bear
Mister Bear
My Uncle Terwilliger Waltzes with Bears
Oh Boy Do I Love Bears
Polar Bear and Crocodile
Smokey the Bear
Sometimes That Bear Bites You
Teddy Bear
Teddy Bears’ Picnic
Teddy Bears’ Rave-Up
The Bear Song
The Big Brown Bear
The Death of the Bear
The Grizzly Bear Song
The Preacher and the Bear
The Teddy Bear’s Head
The Three Bears
Waltzing with Bears