Assuming the time table of Wrath of the Lich King's pre-patch and release will be similar to that of The Burning Crusade, we're probably looking at an early to mid October release with patch 3.0.2. The 2.0.1 patch hit on December 5th, 2006. The Burning Crusade went live January 16th, 2007. The gap was slightly over a month. Assuming Wrath makes its release date of November 13th, early October is a really safe bet. This means you have a little less than 30 days to finish the things that are going away when that patch hits. Specifically: Your Amani War Bear.
Whether your guild is on the cusp of getting their first bear or you're in the queue to get your turn (or even if you're looking to buy a bear from a raid group), time is short. Remember that Zul'Aman is only on a 3 day lockout, not 7 like most raids. Most groups only run the place once a week regardless, but you may want to consider rallying your raid to push for twice a week until patch 3.0.2 hits. You may only have 8 or 9 raid resets left before you're out of luck. I very strongly recommend WoW Insider's Zul'Aman Bear Run guide from our Jennie Lees if you just need to shave off those last few minutes.
Good luck, ladies and gentlemen. I hope to see many bear mounts in your future.