When you refrigerate bananas the bananas will last from 2 to 3 weeks.
Bananas do not really require refrigeration and you can safely leave bananas out at room temperature and they will last a week and sometimes longer.
But refrigerating bananas help to keep the bananas fresher longer and if you do want to keep the bananas fresher longer then refrigerating the bananas is a good idea.
Sometimes I'll buy extra bananas that are on sale and refrigerate the extras even though I eat bananas a lot so I can eat a bundle of bananas within a few days.
Some of the bananas I have are eaten up when refrigerated within a month at most.
Even when bananas start turning brown or black and mushy they still are safe to eat but not as appetizing.