One of the first rules of
budget conscious cruising is losing your attachment to your home foods and brands (no matter what home you be from!) and go with what the locals eat.
The Bahamas are
not a very expensive place to eat, if you shop carefully.
One of the challenges in the Bahamas compared to many of the
Caribbean islands is that they have almost no indigenous agricultural anymore, so you have to plan you grocery visits around the time of the supply
boat if you want fresh veg.
As somebody has already mentioned, on the
remote out islands with smaller populations, the locals all order their
food in. What stores there are are small and poorly stocked. You learn to stock up in the population centers, and do the best you can in the
remote spots.
Learn whats local. Just the other day, my partner was in the supermarket here in
Grenada, and voiced her (mild) frustration that there wasn't any ginger root on the shelves...again! A woman turned to her and said, "Honey, it's been raining for 3 days! Who wants to go out in those muddy fields and dig them roots?"