When you enter Nimbasa City you will have to fight some Team Plasma Grunts that are assaulting a old man. After you save him, he will give you a bike for a reward.
Note:This old man is also the Day-Care Man.
You get it from the daycare man in nimbasa city after you defeat some plasma grunts who are harrasing him. As a prize for saving him he gives you the bike.