First off the 1 hour you have left yourself is likely not to be enough and here is why.
Most people who travel on Saturday to the Bahamas are traveling to start their vacation in one of the resorts on the islands and flights are likely to be full on that day. Keeping that in mind you should realize that most people by the time they arrive are already in the Vacation mode and are operating in "brain off" state. When you arrive to Bahamas from outside you will have to go through immigration and unless you hold Bahamian citizenship or residency you go in the line with everyone. And given the number of flights arriving around the time you will be arriving you will be in line with about 400 people.
One of the things I was watching when I stood in that line was that people in their vacation mode don't listen to the flight crews telling them to fill out arrival cards for every member of the family, which they don't do nor do they fill out all required parts. So what starts to happen is that people will be filling out those cards as they stand in front of the immigration officer delaying the line. So for us we have arrived at 11:40 but left the airport close to 2pm.
Once you get through that line you will have to collect you luggage, which hopefully makes it to the belt and then through the customs which will make it more or less a formality but still takes time and then re-check to the domestic flight to North Eleuthera.
So all in all I'd leave myself more time then 1 hour to make the flight.