Let's start with an analogy, not only because I have faith that my readers understand analogies, but also because you're guaranteed to understand this one:
Jedi is to lightsabre as Steampunk is to Bartitsu
Jedi don't have to use lightsabres (in fact, I'm surprised there aren't more who eschew them), it's just appropriate and therefore common. And your Steampunk character might choose to fight with a steam-powered bazooka but it's not, shall we say, canon.
So, let's investigate Steampunk and how characters fight in that milieu: canes, flintlock pistols, smallswords and sabres for weapons, fisticuffs, shin kicks and wrist-locks when unarmed.
Steampunk Movies
Click over to SteampunkMovies.com, a site launched just this January to address all your steam-powered film needs. The site is still getting started, but I'm sure you'll find more there soon.
If you're unclear on the Steampunk concept, that site pointed me to a clip from the TV show Castle (Season 3, Episode 4):
And although almost universally derided, you can't avoid talking about the popularization of Steampunk without the Wild Wild West:
And the original series from 1965 that "inspired" the movie:
Wondermark!
My favourite web-comic, though I admit the Bartitsu content is lacking. As they say, "Think of England":
Lady Sabre & The Pirates of the Ineffable Aether
This web-comic is really the way to go for the Steampunk afficionado. Here's their most recent page, but you should really read it from the beginning:
http://www.ineffableaether.com/
The Steampunk Community
If you're the type to tinker, enjoy vintage-futurism and Victorian style, and maybe want to use your Bartitsu with friends in costume, consider these groups:
- VSteam: Vancouver Steampunk at SteampunkCanada
- Steampunk Fashion Livejournal
- Brass Goggles, and their great forum
- Seach Facebook and Meetup.com for a group near you (many major cities have one)