In Japan there are almost only private buses. many are run by and around the private train companies as a way to get their trains to be more useful to more people like when a 25 minute walk from the closest station is a 10 minute bus ride and the busses come often enough to be convenient
That's interesting - the main Dutch train company provides dirt cheap bike rentals for the same reason. (For arrivals only; people can use their own bikes to get to the station.)
The train companies in Japan, while private in name, can only be described as hybrid. They have massive gvmt concessions for land to build their malls and make profit. The gvmt also has a lot of direct and indirect influence on them (and the other way around). In fact I'm literally now in one cafe in one of those malls, I haven't used the train today but still a part of my money goes to the train company thanks to these concessions.
I'm not complaining BTW, love the train system here, it's only when someone tries to describe them as either a purely "private" or "public" company it's never so straightforward IMHO, so wanted to clarify.