In the USA, there are many kinds busses that are not public transit. Greyhound and Trailways were historically the most famous, but there are still lots of long and intermediate distance services (i.e. not just shuttling you around a town) that are still completely private bus services. Today, Megabus and Bolt would be contemporary examples. They are subject to some regulation as a kind of "public transportation", but their services, facilities, investment and staff are in any significant way controlled by governments.