I don't know what the Bahamian authorities will do about this.  I know
what a private boat does about entering the country, and it is assumed
that you will leave with the boat which has to pay an entry fee ($150
to $300 depending on the length of the boat).  What they will do about
passengers being carried only one way I don't know.  Ask.  

I've crossed from the Keys to Bimini, from Miami to Bimini, from West
End to Fort Pierce and from Lucaya to Miami.  In a VERY slow sailboat
that motors at about 5 knots.  It never took more than about 14 hours
and was only overnight because we didn't want to get to the Bahamas in
the dark.    

Going east, we'd leave about 1700 or so - light enough so we could see
to get around any reefs, and get to Bimini at dawn (and then have to
wait for high tide to get into the harbor).  Going west from Lucaya
with no wind, just motoring, we left at 7ish and hit - err - arrived
offshore near Ft. Lauderdale at midnight.  Going from West End to Ft.
Pierce we had a steady 25 knot wind and the Gulf Stream assisting, so
we were doing up to 12 knots, and we got to Ft. Pierce inlet in 13
hours at just about dusk.

My SIL took his little catamaran fishing boat outboard from Miami to
Grand Bahama in one day, and he came all the way back from the Abacos
to Miami also in one day.  Of course he has two big engines and we've
only got one and a big heavy boat.

Note:  Depending on where you want to be on Grand Bahama, it would be
better NOT to aim for West End because it costs much more to get
transport from there to anywhere else.  I think a taxi is about $30.

grandma Rosalie