Food in the Bahamas is much more expensive, there is no way around this fact. Now, if you are going to pay more, you might as well get better food for your money.
We have found that the produce sold at the local grocery stores, while more expensive, is pathetic. Apples have brown spots on them, lettuce is already wilted and rotting. You pick through and hope to fill your basket with enough good produce to make a nice salad back on the boat.
We then discovered that the marinas who cater to the very wealthy have "mini grocery stores" in them. The brands of food on the walls are those sold in Costco in the United States. What they do is send a fast boat to the US to stock up, then run back to the marina to supply the shelves. This means that you are getting American portions at Bahamian prices, but most of all, fresher foods.
The selection and bulk may be limited, but we have found that the foods are of wonderful quality and it is easy to fill up your stores with fresh and wonderful produce.