When I was a kid we rode away from cops on our bicycles often. We had offroad areas into which we could flee, pedestrian bridges, etc.
On the motorcycle boards running from the cops is a real and live topic, much discussed. It's easy for many riders on newer bikes to get away from police nowadays. A lot of bikers hide the plate up underneath the rear fender, and have kill switches for their lights. Rather than pay a ticket, many riders would rather open the throttle and be done with it.
I would guess it would be hard for police to mount a real pursuit of a bicyclist in an urban environment, with heavy traffic. Lucky for most bicyclists police almost never chase them.