«идёт» is used for:
- one-way motion on foot
- one-way motion within your city (e.g., to work, to school, to the movies)—едет is also OK if you want to specify the means of doing so
- when talking about the routes of public transportation, also not required (but quite idiomatic)
Well, it is almost not a motion verb here. The distinction идёт / не идёт is not about a real motion at a certain moment but whether the path the vehicle takes, the planned route connects the two points. If it does, the bus eventually ends up where you say it идёт.
The plan either includes the bus going from A to B through a certain sequence of intermediary points or it does not. The vehicle may finish half-way, it may actually go in the opposite direction (from B to A)–or go to a totally different destination C instead. This is the sort of context where идти operated on public transportation: distinguishing vehicles going to different places.
In formal speech the verb следовать may be used to express the same thing (e.g., "Поезд (про)следует до станции Нара со всеми остановками, кроме: Матвеевская, Мичуринец, Дачная"). It is pretty much limited to train announcements, akin to how English speakers rarely say that trains "terminate" somewhere.
«Е́дет» is OK too. Generally, we use «идти́» for going by ourselves, and «е́хать» for going using a vehicle. Vehicles are an edge case, so both words can be used for them.
So what you're saying is, we could use идти or ехать, both of which are unidirectional verbs of motion, to say that a bus goes on a route (will go one way and come back)? If I am understanding correctly (and it is just as likely I'm confused), then I suppose I could technically think of the bus as not going on a route, but really going one direction: in a loop, straight back to where it started.
You’re right, идёт and едет refers to uni-directional single movement. However, any repeated movement is composed of many uni-directional movements, so it’s perfectly OK to use it for buses going on a route, too.
«В город» means the bus is not in the city, and city is its destination. (For example, it goes between two cities.). So, «Э́тот авто́бус е́дет в го́род» means 'This bus goes to the city'.
«В городе» means the bus doesn't leave the city, that its route is inside the city. So, «Э́тот авто́бус е́дет в го́роде» is closer to 'This bus goes in the city'. It sounds somewhat unnatural.
I responded "This is the bus that goes to the city" but I now realize that "this is" should be "Ето", right?