Ideally you'd want a 3CCD camera. However, the cheapest they tend to run are roughly $700 or so.
Anything below $600 will net you a basic, run-of-the-mill camcorder. Try to get one that records on the Mini-DV format. Hi-8 and S-VHS, though cheaper, give fairly low quality recordings. DVD and Hard Drive recorders are a lot more expensive and only gives you a restricted recording space... often much less than that offered for tape-based cameras.
If you're going to want a relatively steady shot, then you might be scapping the edges of the barrel trying to find a good camera. You'll need something equipped with an internal digital steady cam option. At that price range, they may not necessarily be all that great. And, remember, if you're going to be filming while on your bike, it'll be shaky even if you have a proper optical stabilizer.
Another thing, don't even take a camera's "Digital zoom" number into count. Always look at the optical zoom.
Camera brands in the higher end of the low-budget spectrum that I would recommend are JVC and Panasonic.
One camera I would recommend is the Sony DCR-HC21.
I'm typically more of a Canon fan over Sony but at this price range, I'd take a Sony instead.