I make my living in photography and video, so you may find a few good video cameras in your range, maybe the used market. Start shopping by first getting a "quick" education in the features you need, vs the price. Lets look at low light. Low light capability in the cheaper range can cause the video to look grainy, off colored or nearly black and white, generally sloppy looking. It can be somewhat usable, if you don't require a super image. For the sake of rider review, it should be ok. With regard to an "education", go look at places like B and H photo (NYC), and compare the reviews of the cameras you think will work, and see what the pros and cons say... One example of "decent" lower light capanilty (I do not own or have I used this camera, just have heard it's ok) is the"JVC GR-DA30 Mini DV Camcorder" which use small digital video cassettes, and for the dollar amount you have it may be one of the possibilities. You will have to do some homework, and if you don't quite understand some of the specifications, google it, and read up on it. Education of what you are buying, is invaluable.
One more thing, since you are going to record yourself, with no camera operator, you will need a tripod. This way, you set the "zoom" as wide as the ring area, press record and the tripod will hold the camera steady for you. I can also add, that when the sun is out, (and the sun is behind the camera, the camera should never look at the sun) and you are riding outdoors, the images will be much much better...good luck -Lw