Hikemor made some good points. If you are not conditioned for bike riding, attempting a bug-out by bike is going to leave your body in some hurt and in more places then you do not want to contemplate.

As for the concept of pushing a bike loaded with gear, a bit of a reality check is needed. This reality check is simple; most people cannot walk 10-20 miles on any given day, let alone while humping a 25-40 lb pack or pushing a fully laden bike, ala the 1960's era picture that Les posted...even on paved streets or paved roads. The human body needs to be trained for walking long distances especially if your bug-out plans include walking for multiple days, otherwise your whole body will suffer, especially your back, legs and feet.