Regarding New York bridges ~ they're all owned and operated by the New York Port Authority ~ an independent interstate compact operation. For all practical purposes they are a pay as you go sort of thing, fairly close to what you'd get with a private bridge company!
I was referring specifically to the road. The bridges in New York are marvels of engineering - and free as long as you’re walking or biking. The one that concerns me is the Manhattan Bridge and repeated torsion stress imposed by subways. Two trains on opposite sides of the bridge must cross at the same time to counterbalance the torsion, but the maximum stress when they first enter exacts a metal fatigue toll over time.