Origin/reason for the expression "on the bus" instead of "in the bus"

This is sort of a follow up to my question here.

I was told a while ago that the reason why we use "on the bus" instead of "in the bus" is because back in the day buses were open, that is, they didn't have a roof.

Is this story correct or is there another reason why the correct expression is "on the bus", in spite of the fact that when one gets on the bus, he is actually inside the bus?

I doubt that story. It's hard for me to imagine how one would verify it in any case.

Notice that mass transportation generally uses "on". "On the bus", "on the train", "on the plane".

On the other hand, cars and small recreational airplanes would be "in". While small vehicles that are not enclosed are "on": "on the bike" "on the motorcycle", etc.

My intuition is that it has something to do with the notion of boarding or embarking. I would never say I boarded my car. But to board something is basically to "step onto" something. Again, it depends on how the event is conceptualized. There may be a historical explanation, but again I would be wary of them without substantial empirical support.

Having said that, I think the more likely historical explanation would be that "on" is used for mass transit by analogy with traveling by boat -- the first form of mass transportation.

It is less about "on the bus" and more about the meaning of "get on":

1. (transitive) To board or mount (something), especially a vehicle.
   Please get on the bus as quickly as possible.
   .
2. (intransitive) To enter a vehicle.
   She has no trouble getting off a bus but has difficulty getting on.

One of the antonyms for "get on" would of course be... "get off".

1. To disembark from mass transportation, such as a bus or train.
   You get off the train at the third stop.

The Visual Thesaurus illustrates many other definitions of "get on", including a social aspect (getting along with), which is why:

• the British situation comedy of the 70' was called "On The Buses" (not "in the buses"...)

You did not just get in a bus, but also on an adventure with people you were about to interact with.

• an association about "reuniting incarcerated moms and dads with their children once a year near Mother's Day and Father's Day" is called On The Bus.