Bikes can be hires in most towns and villages, just ask around; the quality varies but there are some reasonable machines out there. If you are staying long term there are several shops in Koh Samui that stock authentic bikes and they can usually be sold on before you go home. Prices range between 80 Baht to 120 Baht per day (prices are negotiable on monthly rentals.)
Apart from Ban Khai to Thongsala and on to Haad Yao, the island is predominantly hilly, thus be prepared for a work out if you cycle elsewhere. Always remember take plenty of water, head wear (helmet advised-the hills give you a lot of speed) and sun-cream.