I have sailed back and forth between USVI and BVI on our boat (which is in charter). I believe customs in BVI treated us same as privately owned (without being in charter) and no problems. We often pick up(and/or dob off) friends and family in USVI before heading to BVI and just pay the regular fees/ National Park permit Cruising fees.

I would believe you will have no issues.

Now if the boat is privately owned charter boat based in USVI, I would be hesitant of going to BVI without commercial paperwork, or email from BVI clearly stating what expectations are .