We saw it after Tropical Storm Sandy on the east coast this year. Public transit was flooded and at a standstill, even for weeks after the storm passed. People took to their bikes to get supplies and to get where they needed to go.
This article says simply owning a bike and using it regularly increases your ability to deal with any kind of disaster because you are more likely to be fit and healthy, prepared for physical and mental challenges and you can cover considerable distances by bicycle even when roads are closed to cars and mass transit. Here's more on how your bike could help you fend for yourself in the case of disasters of all kinds.