Yes, it's possible to play Zombies, Run! if you're on a bicycle. It'll still be able to track your route via GPS (but not Accelerometer/Step Counter) and you'll still hear the story and music. However, depending on your speed, you may be travelling too fast on your bike for the zombie chases!
Remember, it's extra important to pay attention to the road when you're cycling with Zombies, Run!, especially if you have headphones in.