The DW and I don't own a car. Our bug out gear is touring bike ready and our multiple planned routes out of town include bike paths and roads compatible with bike travel. Our average travel speed on the road is around 18 - 20 mph. Our freeways around here are backed up daily at rush hour I would hate to be stuck on one of them during an emergency evacuation.
Not owning a car does not necessarily equal being unprepared.
I don't own a car and am a cyclist too. As a cyclist i think there are many advantages over cars.
I can happily cycle a 100 miles a day at around 20 mph and at a push can do a 200 mile day.
If on roads with traffic jams i can cut trough the traffic still doing 20mph.
I am not reliant on the range of the fuel tank and don't have to worry about empty gas stations.
I don't have to worry about the car breaking down or over heating, bikes are simple to look after.
I am not restricted to only roads, i can go across country and cycle through cordons and closed roads.
My fitness level is probably a lot higher than the average car owners fitness which equates to survival fitness and control of survival stresses.
Not owning a car definitely does not mean you are unprepared or that you cant look after yourself and that you are a burden on others.