It's a good question. I'd have to say either can be correct -- as you point out, people ride on the bus, but this doesn't necessarily apply to objects that can be inside the bus. It's more a matter of preference and of context.
I can't find my phone?
Did you leave it in/on the bus?
There's a kid's song, it goes something like, "The wheels on the bus go 'round and 'round, 'round and 'round, 'round and 'round'"
I'm going to get there early to make sure we get a seat on the bus.
To a certain extent, objects that are part of the bus are on the bus, and those which can be removed are either in or on the bus. But I don't think this is any kind of rule, and there may be exceptions.