First off, a usb extension cable would work lol, would be funny though. Do not go more than 10ft, unless you buy a cable that boosts the band signal.
Some routers allow you to do a wireless-wireless bridge, but I am going to go ahead and tell you no. In order to do what you are asking, it either requires hacked firmware on specific router models, or hundreds of dollars to buy hardware made to do that.
If you don't mind using extension cables, an alternate to what you are asking is to forget the usb wireless adapter on the 360, and go with something like
this $50 device.
IMO, the 360 USB adapter is over priced. It is plug-and-play, that is the only reason for its price. For anyone who is a tiny bit techy, they can use a standard wireless bridge which works with anything that has an Ethernet port, so it is not limited to a single device. Basically, you connect that to your 360's Ethernet port with an Ethernet cable. Then, you can use any. Then, use a long ethernet cable to extend the wireless instead of a USB port.