Fifty miles a day on a bike is actually quite easy - given a good bike and a conditioned rider with some experience. Fifty miles would be tough for a neophyte.

If I ever pack a bugout vehicle, my touring bike will be included, because a bike can go when and where a car cannot, can travel self contained, and can cover a surprising distance, given the proper motivation.

My preferences are a touring frame with wider tires (37cm), low gearing (around 20 inch to grind up hills),front and rear bags as well as a personal waist pack, helmet and riding gloves, properly mated shorts and bike seat, dark glasses, and lots of water and energy food. You can easily pack forty pounds of gear, food and water, but compared to backpacking, you can cover five times as much distance. Count on a sore butt.
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Geezer in Chief