Well obviously you have to ride a bike on the same side of the road that you would drive on. I wouldn't recommend it though, especially if you're not used to the roads and driving system, e.g. roundabouts, which seem to confuse Americans an awful lot. The roads in and around Georgetown are more like a big city than a small island and there's a big problem with driving recklessly and under the influence. The road casualty rate is much higher than in Europe.
If you want alcohol and cigarettes, buy them in duty free before you fly to save a small fortune!