But if you're driving a car, the fastest route may be longer than the fastest cycling route, because you can take advantage of high-speed roads (highways) that cyclists aren't allowed to use, even if that adds a few miles to the route.
Not being allowed to use a highspeed route that adds miles is not an issue for cyclists, whose speed and distance is limited by physical stamina rather than posted speed limits.
Other than that, I don't necessarily agree that it is all that much different for a transit commuter than a bike commuter as far as their knowledge of the map. They each know different maps. Transit users know transit maps, bike commuters know their own route maps, and may be totally ignorant of locations and routes one street away from the route they follow. Ask them how to get to 127 Maple street, and they may be clueless, unless it happens to be a street they use.
Having bike commuted for almost 30 years, I can tell you there is a lot of time to think on a bike, and yet large portions of the route are done on autopilot, and you have virtually no recollection of traveling that portion. You remember traffic intensive routes, lane change areas, busy intersection, and bad pavement, but you can often arrive at your destination with no more awareness of what you passed along the way than the transit rider.