Flight is the best option to reach USVI. Although you can reach there by waterways.
There are no direct flights from Delhi or Mumbai, but there are flights with two stops. British Airlines, AirIndia are few.
Travelling through plane is the most convenient mode of transport. The U.S. Virgin Islands has two major airports - the Henry E. Rohlson Airport on St. Croix and the Cyril E. King Airport on St. Thomas. There are non-stop and connecting flight available from the U.S. Mainland to St. Croix and St. Thomas.
no car routes
no bus route
You can reach USVI by waterways. The option of heading to St. Thomas on a cruise ship or availing the reliable, regular ferry service is the only option.
The best way to get around in USVI is by car, rented or your own or even a cab.