The question is a paradox because "literally" is an oxymoron and you said you already know what the sentence means, so you do pressumably have some pragmatic understanding of the phrase. That said, I agree that it is questionable.
It is basically a noun used as prepositional adverb, cp. on-line, thus likewise anschluss. This is a clumsy interpretation: The verbal phrase with haben is a circumlocution because there is no verb that would entail the complex requirements of politeness and direction at once. The usual verb for the intended action is umsteigen, which is not available in this case when some passengers would rather not continue their ride. At any rate, it cannot be interpreted as a bare noun because the Anschluss, ie. the connection, is not anything one could have in possess.
Haben is frequently used this way, e.g. as einen schönen Abend haben. With Abend it should be clear that it is predominantly the head of an adverb of time (am Abend, Abends, allabendlich), while schön is the topic (thus sometimes elided, "Dann mach dir noch einen Schönen.")
This is not to be confused with the adverbial participle anschließend < anschließen "to connect", because you do not connect yourself to the bus.
An interesting correlate is the fact that Bus is short for Omnibus, from the accusative of omnis (all, everything, -one), thus meaning "for all" in Latin, i.e. public transport. Which is bulls, I think, but that doesn't matter. Transport between computer parts is also layed out around a data-bus, with a logical resemblence to streets. In either case there is a terminal at the end of the line. Perhaps that's why im Anschluss can mean at the end of the tour.
Pressuming that im / am < ham > haben, from Old Frankish ham "with", compare Latin cum, com- (as in connect), German participle ge-; it may be argued that "mit Anschluss an" is the current northern equivalent.