IMO there should be a lot more bikes in Zombie movies / books, or anything else post-apocalyptic.

If civilization collapses, you’re not going to be able to get gas for your internal combustion engine. Gas has a pretty short shelf life, so even if you stocked up you’d be running out soon. If you have something electric you’re better off, but charging those to full without a working grid will take multiple days on home solar panels.

Chances are the streets will also be filled with vehicles. A big vehicle like a car is going to have trouble getting through. A bike will squeeze through much smaller gaps. And, if necessary you can lift it up and over something.