In addition to the open air market, there are several little shops on Bimini. Their merchandise is variable. Usually they carry soft drinks and snacks, some other food and some clothing.
What to buy: I went to get postcards. I went to several shops, and found the following ones.
The Beach (a good one)
The docks with fishing boats (good)
The Compleat Angler (good)
The bank (yes really)
The Baptist church (uninspiring)
Another church (ditto)
The cement ship that is disintegrating off the island (VERY ugly)