In his book “The Zombie Survival Guide: Complete Protection from the Living Dead,” Max Brooks has dedicated a section to the pros and cons of several different types of vehicles that can be used to evade zombies. I was quite happy to see that the bicycle ranked as the hands-down favorite land-based vehicle (only the hot-air balloon was a better choice overall.)
The relevant verbiage:
In a class by itself, this vehicle offers the best of both worlds [the silence of the horse, and the mobility of the dirt bike]. The common bicycle is fast, quiet, muscle-powered, and easy to maintain. Add to this the additional advantage that it is the only vehicle you can pick up and carry if the terrain gets too rough. People using bicycles to escape from [zombie] infested areas have almost always fared better than those on foot.
I got this book in the buy-one-get-one-free rack at the bookstore, and it is actually surprisingly good, despite the silly subject matter.