My last trip there at that time of year (Early January) was 8 years ago and was to the New Providence area and was land based. At this time, there were large cold fronts moving through that made the air temp 64 degrees F with high winds which was blowing the water out of the pool onto the deck in waves. It did rain but not steadily.
The water temp was also 64 degrees F at the surface.
All that combined cancelled many am dives.
While fronts move through in these months, we think these were colder anomalies but it does happen.
I had only brought a 3 mm and a fleece skin to wear underneath and it still was not enough.
For reference, in calm, reasonably warm sunny weather, I can go to about 74-76 F water temp in surf shorts and still not be terribly cold. Water temps of 64 F gave a bit of a shock on entry then being cold during the SI and return trip with wind.
I might consider going back in Dec/Jan if I were to go further south (out islands) or choosing a different time of year mostly because my wife gets cold in a 3mm in 84 degree F water.
Having just been to Exuma in June, we were told that the fronts still do move through in Dec/Jan/Feb but got the impression they were less severe than northern Bahamas. Since the Atlantic is not far away a bigger storm would create heavier seas - north or south.
You can roll the dice and get fantastic weather (or not).