A few rags:

"Grizzly Bear Rag" (1910) by George Botsford, words by Irving Berlin
rag: https://www.youtube.com/watch?v=sytjYXv2tHA
song excerpt: https://www.youtube.com/watch?v=qK-EpDCvOuY
full song: https://www.youtube.com/watch?v=tdfJT7NreSc
sheet music PDF

"Polar Bear Rag" (1910) by George P. Howard
https://www.youtube.com/watch?v=r45zzLHDK3Q
https://www.youtube.com/watch?v=gHmfZpW0xTo

Another "Polar Bear Rag"
https://www.youtube.com/watch?v=BclS-NDDM94"

Also:

"That Society Bear" (song, 1912) by Irving Berlin
https://www.youtube.com/watch?v=KiNCbnswP0A
sheet music PDF

"Fuzzy Wuzzy" (song, 1944)
https://www.youtube.com/watch?v=nwmBuPBrJ1Q

Let's not forget the panda; for instance, "The Panda" by Hall and Tait, and "There Once Was a Panda", both of which you can find with a Mudcat search.

You can find a wealth of poems about bears (or anything else) at allpoetry.com.