When I've had to peel a bunch, I work in stages:
Top and tail every banana
Slit peel on every banana from one end to the other
Use thumbs to split open peel and invert over a bowl
You can rip through a whole case of bananas rather quickly that way.
Although it surprises me a bit that three bags are not enough, Ziploc bags do in fact not form an absolutely gas tight seal. If you have the means, you can try vacuum-sealing the bananas, or pack them in a container that actually has a proper seal/gasket.
If this still does not help, try packing them in a glass or metal container (again, with a positive ...