Yep, you need a wireless bridge. My my first thought was also an airport express: http://www.apple.com/airportexpress/

It'll certainly work, I've done similar things myself with one, but it will need to be configure to join the wireless network first. One benefit is that it has wider use: you can, for example, plug many types of printers into it or connect it to a hifi/speakers in order to have wireless printing and audio from computers on the wireless network. Or it's just a more useful device to have left over when you later wind up not needing to connect the TV.