A number of sailing schools from the mainland offer winter learn to sail courses in the BVIs.

I have done my basic and intermediate courses on two separate trips from two different schools to the BVIs (in 1999 & 2014). One happened to be where I live and the other was not. It doesn't really matter where the school's home base is located as long as they have the certified instructors, teach the course you want to take and, quite frankly,you trust them enough to hand over money 5-6 months before you go.

I live in Canada so I look for courses that are affiliated with the CYA (Canadian Yachting Association) which is the equvalent of the ASA.

If you do a course and are planning to write an exam and get certification from it, I would make sure the organization you go with has the courses aligned with the national body of where you live (Canada, the U.S., etc). To that end, the skippers/instructors have to be certified as well.

cs