Ovidiu's response is, as usual, very helpful and entirely accurate. Being a non-native speaker, here are some additional things that it took a moment for me to wrap my mind around: the use of the definite article here is different from what we would expect in English, and is in some ways a bit of an exception in Romanian too. Generally in Romanian nouns after (aka governed by) a preposition are in their 'nearticulat' (without-an-article) form, but means of transport after 'cu' are one of the exceptions. "el a venit cu taxiul" = "he came by taxi" and probably not "he came with THE taxi", just as Ovidiu explained. So, two important things, both about the definite article on "autobuzul": one, generally speaking in Romanian one does NOT see a definite article after a preposition except in a handful of exceptions, this being one. two, contrary to what it sounds like, this use of the definite article is NOT defining a specific bus ("THE bus"), as a word-for-word (motamo) translation would wrongly imply.
As stated by others, if the Romanian can mean he comes as a passenger on the bus, then "He comes on the bus" and "He comes by (the) bus" need to be accepted, as these are ways you say that in English. "He comes with the bus" means that he brings the bus, as in, he drives it here.