450cc enduro (dirt bike, scrambler, motorcross or whatever you want to call it). Something like a WRF450.

Will out-accelerate any police car, can easily hop over kerbs, grass verges or much more, can go down narrow footpaths, can U-turn on a dime, can hide in woodland, and with a proper enduro fuel tank it will keep going long after the helicopter has to go and refuel.

As a kid I often managed to lose police cars on a 80cc and a 125cc, whereas a 400 or 650 will blow away most police cars even on the highway. Eventually a fast car can catch up, as such bikes are for acceleration and torque rather than top speed, but it's super-easy to just go up on the grass and do a U turn, vanish down an alley, just ride over a ditch etc.

You can - and I have - literally just duck down and hide behind a parked car.

The only way you can get caught on such a bike is by being a pussy or an idiot, such as trying to outrun on the highway, where you don't have the aerodynamics, or by being too stupid to use its ability to simply go off-road, between bollards etc etc.