We chartered from BVI Yacht Charters (right next to Moorings) in February. There was a driver who offered free rides to both Pussers restaurant and OneMart. I guess he was paid by them, and he heavily promoted them. We decided to take him up on OneMart, and it turned out fine. He drove us in both directions, and waited while we did our shopping.
Before that I walked to Riteway and back, just to grab a few items. It's a short walk, but involves crossing some rough ground and avoiding cars. I don't think I'd want to do it with a shopping cart.
Dan
