My initial emphasis in this thread was on a bike's utility in getting home from work if something happened that would cause massive gridlock or make roads impassable (such as an earthquake that damaged bridges and overpasses). Riding a bike in that scenario would beat walking, by a long shot. And my bike is light enough that I can lift it and walk with it for a bit if need be.
For getting around town in the aftermath of an event in which gas may be in short supply or streets may be blocked by fallen trees, yes, a bike would be terrific for that, too. Bikes are popular in my neighborhood every day of the week for running errands, because car parking is in perpetual short supply.
Like my camping gear (and teardrop trailer), I bought bikes for recreation. Like camping gear, bikes have a lot of utility for preparedness.
For anyone concerned about bug out scenarios, bikes are the alternative to gas-powered vehicles and hoofing it. And they can easily be carried on a vehicle.
BTW, I have bear spray from Cabela's that comes in a neoprene holder that fits snugly on a handlebar grip.