Bridging is not what you want to do. That combines 2 connections to the same LAN into one. Not 2 connections from different LAN's.
First, you need to setup ICS on the laptop to share out the wireless connection.
rightclick "network places">"properties", rightclick "wireless connection">"properties", "Advanced">"share this connection" (or however they word it) Then walk through the quick wizard. This basically turns your laptop into a router, making the wireless connection the WAN side, and the ethernet connection the LAN side.
Now, to get this to work right, you'll have to turn off DHCP on your router, so that the desktop is getting it's IP/mask/gateway/etc from the laptop's ICS, otherwise the 2 are fighting each other to give away IP's.
It *might* work if you plug the cable from your laptop into the router's WAN port, and leave the router's DHCP enabled. I haven't tried that, but in theory it should work. Of course, then you'd have some weird double NAT thing going on and that could possibly mess with some of your programs. No, actually that would be a triple NAT, if you count the originating wireless AP. Confusing, isn't it?