In most cities with good bike infrastructure I've seen you cannot ride a bike among pedestrians, they are limited to roads and bike lanes[0]. Whenever I see bicycle on a sidewalk is most often because road is jammed with cars or it's too dangerous for bikes, if we get rid of (most) cars, this will not be a problem as there will be plenty of space for everyone.

0. http://www.cambridgema.gov/~/media/Images/CDD/Transportation...