I am a cyclist, so I read this thread with interest. However I don't consider bikes a reasonable means of bugging out for me. This is because I live in hurricane country so a great amount of distance is needed to properly bug out, and I don't think I would be able to do that with my family. I might be able to ride far enough, if given enough time, but my wife and son could not.
However, after thinking about it I can still see how bikes would be useful in a SHTF scenario. Let's say a person decided to bug in during an event. During whatever event took place (I'm keeping this broad so that it may apply to anybody) lets say that the roads were destroyed or that gas was in low supply or supplies have run out. A bicycle could be used to get around town (to check on friends/family, get supplies, etc.) and get through roads that a car could not get through. This would also save a person's fuel supply for more important things like a generator.
Anyway this is just food for thought for anybody, like me, that didn't consider a bicycle a valuable addition to their preparedness plans.