Bears are epic ground 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 for 750.
A fun loving bear is offered during the Darkmoon Faire by Lhara on Darkmoon Island for 180 .
Black War Bear is rewarded for completing [For The Alliance!] or [For The Horde!], and is directly added to the mount journal.
Vicious War Bear is purchased with a [Vicious Saddle] from Necrolord Sipe or Deathguard Netharian.
The 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.
The Amani Battle Bear is a guaranteed drop from a bag you can loot after rescuing all the scouts in a Zul'Aman timed run in Zul'Aman.
Other bear mounts
The Big Battle Bear is a reward from turning in the code on one of the collectible game cards.