Public transportation and city bike rental systems should be free to ride. We all pay taxes to keep roads maintained, we should all pay taxes to keep public transportation maintained.
Not charging would help busses keep their schedules with less queuing and waiting, tourists would be less likely to rent a car, and it could help that chicken and egg problem. The problem with charging people with riding public transportation is you are taxing the very people we should be rewarding. The people who are committing to taking up less space on the road and living with a smaller carbon footprint are being penalized for their hugely beneficial decision to society not to drive. Making public transportation better and free are the two things that can transform a city and make it more equitable. Poor people would have more money and more places available to spend it. Every city benefits from its people having more money to spend and more places to spend it.