I think that generally depends on the city, but most cities will have what are known as Enterprise funds. This generally applies to things like the Utility Departments (water, power, and some cities even run an internet service provider) where rather than running on taxes these programs need to function almost entirely from funds they bring in for charging for their services. Things like road and sidewalk maintenance wouldn't fall into Enterprise fund operation since there is no active service being rendered that can be charged for, though you could have toll roads but they are exceptionally unpopular in the US.

A bus or rail system could be an Enterprise fund, but it probably depends on where you're at. The public transit system in NYC is an enterprise fund because they have enough usage that they can raise funds from services to cover their costs, but a bus system in a rural city might not be an enterprise fund if it's being used almost solely to provide the elderly or poor with transportation.

In addition to Enterprise funds, US cities operate as businesses (ie they must have balanced budgets and operate within their means, they don't get to act like the federal government and just close down). In most cases if you said we're going to triple the buses/vans but now instead of being revenue neutral it's going to lose money it won't get approved.