About 8-10 days non-stop or an easy 3 weeks stopping in Puerto Rico, DR, Turks and Bahamas. It is usually mostly off the wind with the current and much easier than Florida to BVI. Better done now or in late spring but not too hard anytime other than hurricane season or when the northern winter lows dip down to Florida and the Caribbean and you get north westerlies into the current.
Personally, I would do it non-stop going north of PR
and DR and comming through the Old Bahama Channel between Cuba and Bahamas and go directly to Key West.