It's something like 20NM between the cruise ports at Charlotte Amalie and Roadtown on the same channel so it's really similar diving. There's a cruise operator that doesn't get great reviews on St Thomas or there's 2 that do that both pickup at the cruise port - Admiralty Dive or Blue Island Divers. Dive site selection is often weather dependent but if asked, you could mention Carval Rock and see what they say - probably too far though - maybe too advanced on a mixed boat also. BID has an
interactive map so you can get a sense of some of the options.
Does the cruise line offer some sort of cheap shuttle to Coki Beach? - Coki Dive is there so might be an option for a cheap shore dive if you could find/arrange a buddy in addition to doing your one dive trip on Tortola.
There's 2-3 operators in Roadtown, the cruise operator is one of the better ones - I believe it's Sail Caribbean Divers - and the signature BVI dive is the RMS Rhone, across the channel at Salt Island. Even dive boats from St. John go there weekly - it's a pretty extensive wreck. Easy to penetrate for divers of all levels - big chunks of the sides are missing and the hatch you enter thru is the one Jacquie Bisset exited from in "The Deep" if you're of that generation.
Also Painted Walls is a good dive and we liked anything in the Dog Islands but they may not go there from Roadtown since there's a lot of good sites in/among the other islands near the Rhone.
bviscuba.org lists all your options from Tortola.
I've only dove the East End of St. Thomas and over to the Cays. And most of the BVI's (10 days of all day diving) but if I had to pick one, I'd dive from Tortola. More other things to do on St. Thomas also.
