It will often be a company owned by the state.

In Ireland, most buses are run by CIE, a state company. In Dublin, for the last couple of decades, some routes have been run by GoAhead, a private company (Dublin Bus (part of CIE) and GoAhead tender for the routes). It's been a fascinating experiment in privatisation; the buses all use TFI livery, so the only way to tell whether your route is run by Dublin Bus or GoAhead, besides looking it up, is that if it's Dublin Bus, it'll just be late; if it's GoAhead it won't show up at all. For all that people complain about public sector inefficiency, private companies turn out to be very, very bad at competing with the public sector.