The biggest sports activities in the Virgin Islands are Scuba and Boating. One of the things Tortola is known for is as the home of one of the largest bareboat charter fleets that there is. [A bareboat is a boat that you charter and sail by yourself.]
We did not charter a bareboat (we had a captain and a cook to do that work for us) and we chartered out of the USVI and not out of the BVI. But if you know how to sail, a bareboat charter can be a really nice vacation.
When we did the circumnavigation of Tortola, I did see surfers on some of the beaches on the backside of the island. It might have been Cane Garden Bay or Apple Bay. The waves weren't too big - not as big as on Barbados in the Soup Bowl, but I did see them there.
Apple Bay, Tortola
Located on the north shore, the surf spot breaks with waves 2'-10'. A beach break, with reef bottom. Right and left hand peaks.
Long Bay Beach, Tortola
A good beach for beginners but has a tendency to close out above 3'.
Cane Garden Bay
A point break with the waves wrapping around into the harbour. The waves need to be over 5' before the break is surfable. Size can reach 15'. Beware of exposed reef inside as the water sucks out. Not a safe spot for a beginner.
A left break that is surfable to 12'. The spot is only accessible by boat.
A beach break that is sufable 2 - 8'. Tough paddle out at times, and closes out easily
Equipment: The surf is seasonal, roughly from mid November to late April, although during the summer months, swells do show up from passing storms on the northern side of the islands. It's wise to bring all of your own surf supplies with you because the one surf shop is some ways away from the surfing spots.