You can purchase a bike here (usually not new) and there is a bike shop, but I would recommend purchasing one in St. Martin. On the French side, there is a legit shop (forgot the name) close to Marigot (near McDonald's) where I purchased mine and took on the ferry with me. The prices are about 200+ Euros but they will take US cash for the same amount! I bought a top of the line Giant bike for $500 and it is still in pristine shape after a year here.