They say that food prices are higher in the Bahamas, and it's true. Nassau is known for having the best prices on foods, as it is the biggest city and has more volume of imports coming to it. While the prices are cheaper than other places, the prices are still higher than stateside prices.
Take a look at these two receipts from different grocery stores.
Taxes here are 7.5%, so the price that is already higher is about to climb even more! It is very easy to spend way more than $100 on a small grocery run, making it very expensive to provision for a long trip here without destroying your cruising budget.