--X-------- wired LAN #1 -----------
--X-------wired LAN #2 --------------
The two bridges communitate over wireless to connect the two LANs. That's what a wireless bridge is for. Generally, wireless bridges will not connect with a wireless AP, because it they did it would confuse the role the bridge is supposed to fill. Did you read the article I referenced?
A quick scan of the article says the bridge you bought is ALSO capable of working in the infrasturcture mode, connecting with access points. If true, you might be able to replace wireless bridge 2 in the diagram with your wireless router. But, I'm not going to read the article for you.
If you only have one computer connected to the bridge, you would be better off with a simple wireless adapter - PCI, USB, PCMCIA card, whatever - take your choice.