Bears are the mainly ground epic mounts, that are obtained from a variety of different ways.
While the rigging on the bears differs between Alliance and Horde, you are only offered your faction's version by
Mei Francis in Dalaran. This will set you back 750 , less any Kirin Tor reputation discount.
Achievement reward bears
Should you complete
or For The Alliance! , the leader of your faction ( For The Horde! Varian Wrynn for the alliance, Thrall for the Horde) will send you this mount. (You might want to avoid the postman for a few days...)
Amani War Bear is a reward from Ashli's Bag for completing the timed event in Zul'Aman on Heroic mode.
White Polar Bear is found (very rarely) in the Hyldnir Spoils bag rewarded for completing one of several daily quests from Gretta the Arbiter in Brunnhildar Village.
Other bear mounts
Big Battle Bear is a reward from turning in the code on one of the collectible game cards.
Big Blizzard Bear was a reward from the BlizzCon 2008 welcome package (or from getting the DirectTV subscription in the USA).