When walking, you spend a good deal of time out of equlibrium, you're center of gravity is not directly over the contact patch of your feet, so as posted, you spend engery supporting your weight. When you're running, there are times when both feet are in the air, so you're actually jumping up and down a bit.
As posted before, on a bicycle, you rest some (usually most) of your weight on the seat and handlebars, so more of your energy is going into just propelling the bike forward.
Also as posted, the gearing is designed to let your leg muscles operate at a speed and force that is optimized.