As Manpot said, taxis will be waiting for you. No need to arrange ahead. Just try to avoid arranging ahead and then taking the first taxi you see if someone is waiting for you. Also, and I don't have any experience with BVIYC, but most of the charter bases will be happy to arrange a taxi to be waiting for you if you let them know your flight number. Copy/pasted below from their website:
BVIYC website FAQWHEN YOU ARRIVE
WHEN WE LAND, HOW WILL WE KNOW WHICH TAXI IS OURS?
If you have pre-ordered a taxi your driver will be waiting for you when you come through arrivals. Although, if there are lots of people around, you can ask for Mike. He will have a sign with our name and logo. The airport here is small and you should not have any problems. However, if for some reason your driver is not there, don’t panic, and don’t even wait. Just jump in any taxi as the rates are standard across the island. You can expect to pay $12 per person, a minimum of $30, from the airport. From the ferry dock, the rate is $5 per person.