Most BVI yacht charters originate in Tortola. However, we have sometimes chartered out of the US Virgin Islands and included both the US BVI in the BVI in our trip. This can sometimes be less expensive, but you must realize that as you go between the USVI and the BVI, you must check in with customs and sometimes a fees.
Tortola has a number of large, supermarket style markets from which you can provision. Many of these are on the water and have docks so that you can take your dinghy directly to the market to pick up and transport provisions. Ask your charter operator about the markets convenient to your boat’s location.
Once you have departed Tortola, small markets are still readily available but tend to have smaller selections and higher prices. So generally it is a good idea to provision as much as possible (including non-perishables) on Tortola. Of course provisioning for a trip in the BVI almost always includes rum, which is a bargain there.