Bananas should last up to a week or 2 weeks without refrigeration or without doing anything to protect them.
But if you do want to keep bananas longer than a week or so and want to keep the bananas from spoiling as fast you can wrap the bananas stems in some plastic wrap.
Wrapping the bananas stems in plastic wrap helps to keep the bananas from spoiling as fast because it prevents the ethylene gas that is produced naturally in the ripening process of the bananas from reaching other parts of the fruit and prematurely ripening it.
So by doing that the bananas won't over ripen and spoil as fast.
You can also keep bananas fresher longer by refrigerating them and they will usually keep for 3 to 4 weeks in the refrigerator.
Even when bananas have over ripened and became mushy and black or brown they are still safe to eat but they just don't taste as good when over ripened.