So I've searched here (and Google) and seen several topics about wireless networking, but haven't seen one where someone's trying to set up a wireless network when they have only one PC. Can this be done? I'd like to just leave the cable modem and wireless router in the bedroom and have my PC in the office with a wireless adapter receiving the signal.
It will will work with only one PC. No problem.
Your wireless router is just sending a signal, it doesn't care how many are receiving it.