Its less than 200 miles, so it shouldnt be a problem, two or three day sail. Provided you get good weather it should be ok. The worst thing is, you have to cross the gulf stream, and after a strong northerly wind, that can take up to three days to settle down, so even when the weather becomes really good, and you have a window of several days, you have to wait at least three days, before sailing. If you are properly equiped, and have enough experience, it would be quite a routine sail. I wouldnt do it without a liferaft, an MF/HF radio, (or a sat phone, but radio is better) and EPIRB. Your VHF and mobile, will go out of range of the coast, at maybe 20 miles if you are lucky, and wont come back into range, until about the same distance from the Bahamas, so for about 120 miles, your only comms, will be MF/HF, or sat phone.
The winds there, can also be problamatic, you get the wind taking you off shore from florida in the evening, but out at sea, they tend to change direction, they go round in a circle, coming from all directions over time, so if you sail with a wind from the south, that wind may change to coming from the west, then move round to the north, and you dont want a north wind going to the bahamas. The gulf stream, will also push you north at a high rate, they say 4-5 knots, but then put a south wind behind that, and i found our drift north, was ten knots. When you are only making 4-5 knots, and your drift north is 10 knots, its adds a lot of time onto your passage.