I tried the exact same card with the exact same computer a few months ago. Long story short, it didn't work, but that may have also been due to the cheap Belkin wireless router I tried to use it with. Eventually, I somehow found an actual app for the Belkin card that brought up a very arcane and confusing screen that as far as I could tell showed the card as receiving a signal, however I still couldn't get anything to work. It looks like it's not directly compatible with the Airport networking standards, at least not on the B&W.
I ended up rearranging the network setup in the house so that the wired D-Link router I had was close enough to the G3 to be plugged in, and then I plugged my new Airport Express ($95 shipped and NIB on ebay) into one of the D-Link's ports and am running my imac G5 and mine and my roommate's ibook G4's off of that. We still have too much sh*t plugged in and running in this house, but at least there aren't cables running around on the floor anymore. 🙂
Don't know for sure what your options are. If it's the only computer you have, I would recommend trying to keep it wired, however if you have other computers that would benefit from wireless and can't set things up the way I have, maybe one of those wireless USB adapters would work. I don't know how those would function on USB 1 ports (which the B&W has), but you could also look into getting a PCI USB 2.0 card. That option may cost you a few bucks more, but it would probably be more reliable.
