How can I speed up banana ripening?
Bananas are imported unripe and then ripened in the country of sale. This ripening is achieved by forcing ethylene gas through the bananas in special pressurised rooms.

Bananas naturally produce ethylene as they ripen, so you could just put them in a sealable plastic bag to contain that gas. Tomatoes also produce ethylene, so you could pop a couple of those in as well, but be aware that they'll also ripen faster too.