Bicycles and three-wheeled bikes offer the same types of advantages and disadvantages that are seen with horseback riding. You will have a nimble, fast way to get around but which restricts how much you will be able to carry in the way of supplies. This means that your Bug-Out Location will have to be much better provisioned.
Since you will be peddling the bike, this means that you will be working harder than riding in a wagon and therefore will need to bring or forage for lots of food and water along the way. But far less than what would be needed for hiking the same way.
Grandpa TJ: Another option for bicycles is to use them as “pack horses”. You can sling a significant amount of gear and supplies on the bike and then just walk it out of the evacuation area. I have heard of refugees packing as much as 200 pounds of gear that way. And you end up with a bicycle to use when it is unpacked. Be sure to include extra inner tubes and patch kits (and tools) in your bug-out supplies if you decide to use bicycles during your evacuation.
Motorcycle Evac
Street bikes, cafe racers and other minimalist motorcycles have the major advantage of being able to “Get outta Dodge” very quickly. Virtually nothing can stop them even to the point of the limited off-road capabilities that they have. But once again, they are very limited in the cargo that can be carried so again, your BOL will need extra supplies to make up for what you cannot bring with you.
Dirt bikes and trail/street bikes take to off-road escapes to levels far beyond those of street bikes. All you have to do is search for videos to see their amazing capabilities.
However with these bikes, you usually have an very small gas tank compared to street bikes which will limit your range between fill-ups.
A touring bike has considerably more storage space and usually much larger gas tanks providing more range that regular bikes. Some are even set up to have towing hitches for small trailers. The motorcycle in the example below has a sidecar in addition to a trailer.
Even homemade trailers can provide significant upgrades to how much you can carry with you although weight is still a factor for the smaller engines in motorcycles.
Off-Road Evac
When it comes to off-road mobility, 3 and 4-wheeled All Terrain Vehicles (ATV’s) and snowmobiles are the kings of moving people and cargo quickly. Although people complain about the noise those vehicles make, what makes them noisy is the way they are being ridden. So if stealth is indicated, keep the engines throttled down to the very minimum rather than running wide open.