Cost for one month is going to be US$600-800. I presume though that you really want to know how much per month for a long period, maybe full time?
If you want to keep a boat in the BVI year round then you have to pay the temporary importation tax. This is ( or was last year ) US$200 for a privately used 40ft boat or US$600 if you are chartering. If you have paid for temporary importation then you don't have to pay for the cruising permit
. Cruising permit
is around US$4 per person aboard per day for a non-BVI registered boat.
If you are a US citizen then the USVI is probably a cheaper option for you.