I've done the crossing many times with two of my motorboats and the weather can be very tricky. Plan plenty of time late spring or summer is a lot less troublesome when it settles down.

Doesn't take much wind to make the Gulf Stream very rough but if you guys give yourself a big enough window for weather you should be fine. As mentioned the crossing is about 50NM.

The boats I have done it with are a 46 Azimut cruising at 25 knots and a 42 MTI so when the window is there it's a short hop. Once there you cab hop from small island to another relatively easily and it's fairly shallow so less susceptible to weather, all you need is a window to come back. Nice marina and place to stay once there with a beautiful marina.
http://www.biminibayresort.com/