I don't think people who ride bikes and don't drive have a totally "free ride". And I would add, even though they don't contribute to air pollution, water pollutio or noise and the are almost never the cause of a traffic death, they are themselves subject to those things that result from car use (BTW: I am NOT against car use).
First, cities levy bond measures to pay for roads that home owners and renters pay for.  Cyclists that don't drive (est: 5%) pay those bonds, so they pay to use the streets. 
Congress has also not fully funded our highways, so has been stealing money from the general fund to pay for roads. That is not from gas taxes as it was promised, but money even from cyclists. So they pay.
Your root issue seems to be that one should pay to use. But what about pedestrians? And, why do the elderly stuck in their homes pay property taxes that go in part for roads even thought they don't drive?