When I saw the video for the first time I thought it was fake - a good edit job.  Turns out no - these bears actually wave, like a human would.  I've never met a bear in the wild so I wouldn't know, but it's got to be something these bears are trained to do. 

These videos are from a wild animal park in Washington state.  I have to claim ignorance on this one folks, I just don't know for sure, but I'm guessing  these bears are trained from cubs to wave to the visitors.  It's not something that looks natural.  It's almost like they're waving their hand and some of them do it with such enthusiasm.

Check out the videos - amazing.