Delta, American, United and Jet Blue all have connecting flights into Beef Island on one of their codeshare/partner airlines, i.e., Seaborne or Cape Air. You can buy your flights to the BVI on one ticket, and they will be responsible for getting you there, even if a previous flight is cancelled or delayed.

Southwest can get you to SJU, but you're on your own after that. BVI Airways, well who knows.