If I wanted a powered bicycle I would get an ATV or a touring motorcycle. The true beauty of a bicycle is that it requires no fuel other than food/water for the rider. As for range, it is all relative and per unit time. There are bike tourist who have ridden around the world several times, and hundreds ride across the country every year. With a gas powered anything you have to be able to get from one fuel supply to another on one tank, or one tank plus whatever you can carry on the vehicle. What if gas isn't available, or available within your range? Reasonable max range for a day on a touring bike is about 100-150 miles, depending on headwinds and elevation changes. The Race Across America riders ride 20 hour plus days and make it across the country in under 7 days. I suppose you are only limited by determination.
Another advantage with bikes is that you aren't stuck in traffic jams with the rest of the fleeing masses. You can happily peddle down the shoulder of the road or other places that auto traffic can't go. In many evacuation scenarios I have little doubt that I could get out of town much more easily on my bike than in my truck (of course I am in the Baltimore/Washington area, so YMMV).
Remember, a bicycle (in it's numorous forms) is the most efficient human powered method of travel. If you can expect an inexhaustable supply of affordable gasoline for any situation in which you will need transportation, then don't worry about a bicycle for a "bug-out" application. If not, then they are a very valid consideration, and can be very useful in non "bug-out" situations as well.
Heck, they are good for you and darn fun to ride too! How can you go wrong? <img src="images/graemlins/grin.gif" alt="" />
Greg