What makes BVI successful?

Wealth. It is a tax haven - GDP per capita is about $48000. Crime follows poverty. Remove poverty and you remove crime. The British Virgin islanders were smart enough to vote to become a tax haven and continue as a tax haven despite pressure from other countries. In other words, once they focused on their own interests, they were fine.

P.S. the Cayman Islands are similarly rich and safe - but they're majority mixed race (African-White). Cayman Islands GDP per capita is the 14th highest in the world. And it is a no income tax place.