While the rigging on the bears differs between Alliance and Horde, you are only offered your faction's version by in Dalaran for 750.
Vicious War Bear (Alliance).jpg
Vicious War Bear (Alliance)
Vicious War Bear (Horde).jpg
Vicious War Bear#Horde (Horde)
The White Polar Bear is found (very rarely) in the bag rewarded for completing one of several daily quests from in Brunnhildar Village.
Other bear mounts
The Big Battle Bear is a reward from turning in the code on one of the collectible game cards.