Mighty Roar
Debutant
I did manage to come across this song by accident on YouTube. A user by the name of "Alfred Cunningham" had uploaded a video detailing the AFL's Centenary Celebrations in 1996 including a 15 minute long medley of all the club songs performed at a special dinner. It included the Brisbane Bears song, which is actually one of my favourites but sadly the video was taken down not that long ago.
Let's fix that, shall we?
AFL Centenary Celebrations - Brisbane Bears Theme Song [Swing Version] - Mike Brady
This makes more sense when you watch the entire performance. As 10Dulkar noted, the AFL's Centenary Ball included a medley of all club songs, each performed in a different musical style by either Mike Brady and The Music Men or club luminaries such as Rex Hunt, Jim Stynes, Tony Liberatore, Sam Newman and Lou Richards.
Brisbane actually got off lightly with this Swing version. Fremantle got stuck with Country & Western and Tigers fans have to endure the Richmond Rap. Fitzroy's theme song isn't too bad, a Parisian Can-Can in keeping with its French origins.
AFL Centenary Celebrations - All Club Theme Songs
Anyway, its kinda-sorta the Bears theme song. Download here: http://www.sendspace.com/file/isxakr
Enjoy!