Do you already have a WiFi router? If so, you can buy another one and set it up as a bridge/AP. Then you connect the 360 to one of the LAN ports on that router. Don't connect anything to it's WAN port. That second router will act as the go-between for your wired ethernet devices in your bedroom.
Or you can get two "ethernet over power line" devices. Those use your house's electrical wiring as the network cable. Here's a link for Netgear's, but there's quite a few other manfs too.