I just bought a used Canon mini DV off ebay for 100 bucks. Make sure you get one that can handle external audio/video (ZR20 to ZR50's) and for convenience, they have a LANC port (to enable remote control).
Used camera 100
bullet camera 40 (mount anywhere on the bike)
Remote mic 12
Lanc cable 30 (not required, but nice to have)