"We are waiting for the bus."
Translation:Wir warten auf den Bus.
In general, whenever a positional preposition isn't literally or metaphorically referring to a place (i.e. when it's used idiomatically), it takes the accusative. You're not literally waiting ‘on’ the bus, ‘auf’ is just the preposition ‘warten’ requires, so you use accusative. In the same way, you're not literally proud ‘on’ her (‘stolz auf sie’), remembering ‘at’ him (‘du erinnerst dich an ihn’), or thinking ‘at’ me (‘du denkst an mich’), so you use the accusative.
It would be incorrect. The construction for “waiting for something/someone” in German is “auf etwas/jemanden warten”. After all, the choice of preposition is pretty arbitrary in both languages. In Italian, for example, the verb for waiting is simply transitive, taking a direct object, like “to await”.