I've had to call CANPASS UK-US when using St. Johns for refuelling, so I would imagine it would also apply when going on to Grand Bahama. If it does, just give them a call an hour or 2 out using the satphone (if you have one, or before take-off if not) with all pax names, passport no.s and an updated eta in local time. St Johns is 2 & 1/2 hours behind GMT in the summer, probably 1 & 1/2 at this time of year. When you land call them again from the handling agents to confirm the details.
The number is +1 888 226 7277
You also need to get a form to be faxed to them with all the details. Calling the above number I guess would be a good starting point to get hold of the form.
Have a good flight