Power available on a quad: I'd be amazed if there isn't 4 amps of 12 VDC -- which is about all a CB would draw during transmit. The radio draws only a few hundred milliamps during receive - maybe a little more if you've got a remote speaker cranked up.
Glen's got a good point about the noise, though -- and I'd suggest speakers built into the helmet. I've got them in the Gold Wing (touring) helmets -- the good ones, suitable for decent quality stereo music -- are less than a hundred bucks for the set. Cheaper ones would work just fine for this application. When you hear a motorcycle passing with the stereo blasting -- it's partly because he wants EVERYONE to know how cool he is, what with music on the bike and all that -- and partly because he's trying to overcome the noise that would otherwise drown out the music. In other words -- he's proving that Glen and I are correct about the background noise. Add a race engine starting off -- and you'll use helmet speakers.
I wouldn't worry too much about having the microphone mounted to the helmet -- a standard mic clipped to the bars, where you could grab it if necessary, should be fine. And cheaper, too.
