It is possible to accelerate the ripening of fruit using naturally produced ethylene gas.
Ripening bananas emit ethylene, so storing unripe bananas in a brown paper bag will trap the ethylene gas and speed up the ripening process. Close up the top of the bag and punch a few small holes to let moisture out.
To ripen the bananas even faster, place a ripe apple in the bag. Apples emit large amounts of ethylene and should generally not be stored with other fruit, as the apple will cause the other fruit to ripen and spoil.
Check inside the bag each day and remove any ripe fruit.
Using this method, we can stagger the ripening of a large bunch of bananas.
It is usually not practical to have a large bunch of bananas become ripe all at once. If you force the ripening of some of the bunch and leave the rest in a fruit bowl, you will have more manageable quantities of usable fruit over a stretch of time.
And less chance of overripe bananas.
For more tips on keeping produce fresh, check out these posts:
Keep Strawberries Fresh Longer
Keep Asparagus Fresh Longer
How to Store Mushrooms
How to Keep Tomatoes Fresh
Keeping Sweet Corn Sweet
How to Store Avocados
Refrigerate It Right: No More Frozen Produce in the Fridge
The Best Way to Store Fresh Herbs
Keep Lemons Fresh Longer