It's only three days from Hilton Head
to Marsh Harbour - within the bounds of dependable weather forecasting. If things still look good as you're approaching the Bahamas
you could easily make Georgetown in another 24 hours under most conditions.
I would head out of Hilton Head perpendicular to the Gulf Stream
and turn south after the GS (look for the GS imagery on-line in advance and watch the sea water
temperature as you go).
I made Norfolk to Marsh Harbour last December in 3-1/2 days last December on my 40, so you should be able to make somewhat better time.