How do you get the bycicle in Pokemon FireRed?

You can't get a bicycle in Pokemon FireRed. The ability to ride a bicycle is only available in Pokemon LeafGreen.

However, in FireRed, you can travel around the world using the running shoes that you get from the Mr. Pokemon in Vermilion City.

While this isn't as fast as a bicycle, it's still a good way to get around the region.