It's a crewed charter. Meaning you own the boat for the week. So they go where you want to go - stay as long as you want to stay, move the boat when you tell them to. Put into port when/where/how long you tell them. It's on the webpage: Yachts with Crew - Virgin Island Sailing Vacations & Yacht Charters World Wide.
In the BVI's there's also the option for Rendezvous Diving. Several dive operators - DiveBVI on Virgin Gorda or several on Tortola will meet you with tanks, Divemaster etc. at a moored location. You set it up in advance and call them on the VHF when you want to dive. I don't think it's much more expensive than their standard rates.
It's an alternative to making frequent stops for fills - most mid-range sailboats don't carry a lot of tanks onboard. That's pretty easy though in the BVI's - DiveBVI has a fill station on their dock in both Spanish Harbor and Leverick Bay. IIRC there's one or two on the other side of the channel on Tortola also.
Personally I'd try to rent a big catamaran - more liveable space between the hulls. We often saw them moored at divesites that we day dove from Virgin Gorda.
Places not to miss: Pusser's Company Store on Marina Cay, Soggy Dollar Bar on Jost Van Dyke - Foxy created the Painkiller there, Foxy's Tabu on Diamond Cay, the beach bar at Little Dix Bay on Gorda (georgeous beach) The Willy T Floating Bar off Norman Island, the Baths off Virgin Gorda and the Beach BBQ friday night at Leverick Bay. On Virgin Gorda there are some beaches only accessible from the water.
Must dive is the Rhone off Salt Island, they filmed the Deep there. It's also remarkably well preserved, 70', has an easy swimthrough and interesting wreck stuff on the stern section. There's also a swimthrough past the 15' high prop. I don't like wrecks especially but I enjoyed two dives there.
This post brings back wonderful memories. My husband and I got certified just so we could take a trip to the BVI. We sailed twice before down there (bareboat - meaning we sailed the boat ourselves). The last time we chartered a crewed cat with diving included in the rate. We got certified here in FL. Since we would be diving on our own in the BVI we wanted to make sure we were comfortable. After cert we did several dives with our dive master friend in West Palm. The we went to the Keys for a long weekend and logged 4 more dives. These were on our own and really helped make us much more comfortable in diving without a DM.
All that said, the BVI diving was amazing. Among my favorite dive spots: Alice's Wonderland, The Rhone, The Dogs and The Indians. Also not to miss: The Baths, Soggy Dollar Bar and snorkeling the Caves at Norman Island and Monkey Point on Guana Island. I joined this board and talked to many knowledgeable people. Another good board, should you decided on the BVI (why wouldn't you?!) is traveltalkonline.com There is a wealth of info there as well.