Look into Pirates Penny/Stormy Petrel - out of Red Hook STT - smaller 12 passenger max - very professional crew and well sorted vessels.
http://www.piratespenny.com/Another option on a larger vessel is Breakaway out of Sapphire Marina.
http://www.visitbreakaway.com/Because of the distances involved I don't think any sailing vessel can get you to the Baths and other islands in a day if you want to spend any time not underway - So you should be looking for a power boat charter.
Most of the charters include a lunch stop somewhere in the BVI, a snorkeling stop and all will stop at C&I in both the BVI and then in the USVI on returning. Some companies offer different trips on different days.
There are some 6 passenger power boats that offer BVI excursions for a private charter, with Captain and fuel costs, C&I and lunch is usually extra as well and it can get fairly expensive but the itinerary is very personalized.
If cost is not a major concern check out Magic Moments in Red Hook.
http://www.yachtmagicmoments.com/rates.htmlIf you are a qualified boater and experienced with exploring new waters there are some companies in Red Hook that offer bareboat power vessels that you can operate and do your own thing. Depending on your travel time and speed the fuel costs can be costly and you will have to do your own C&I in both countries.
In any case it is a long day at sea so make sure any boat you are on has an option for shade underway.