Bluetooth would suck for such a thing (it has almost no "reach", and the farther a person gets from the base, the bandwidth diminishes). Not to mention interference from all sorts of crap (other peoples BT, cell phones etc. etc.).
There's a "sweet" primer here you ought to read:
http://www.sweetwater.com/shop/live-sound/microphones/wireless_buying-guide.php
Now, all you have to do is get a headset and a brick to put on his belt, match the channels and off you go. Yes, it's more expensive than the average BT-headset, but a BT-headset are sure to be a disappointment.
After that, you have to get the audio into the computer: How that works depend of the computer you're going to use. You can use any sort of USB or FW-interface, or you could use the line in. Or you could just use a dedicated digital recorder, copy the file to the computer, and that's it.
That last bit of getting it into the computer/getting it recorded, is a subject in itself. It depends on the solution you choose, the hardware you have, not to mention the thickness of the wallet and how well you want it to sound in the end.