Here is an excerpt:
Bitte steigen Sie an der nächsten Haltestelle aus. Dort haben Sie Anschluss an den Bus Linie 19.
My question concerns the latter sentence. I get the general meaning but still don't understand exactly what this "Anschluss haben" thing means literally. I couldn't find any suitable option in any of the online dictionaries.
Anschluss = connection (also in some other contexts, but not all)
So it means that you have a connection to that other line, that there is a possibility to connect/change to that other line.
"Anschluß" is a loaded word and hence you might not get the usual mileage from dictionaries. Let me explain step by step:
"Anschluß" means "connection", as has been already mentioned by some others. Therefore "Anschluß haben" means you have (the option of) a connection. If you go by train from A to B there might be trains to C, D and E you could get at B because they arrive in B later than your train from A. This is perhaps the meaning you were looking for.
There is also a second meaning: "connector" - the device (or the means) by which a connection is made.
Der Anschluß der Maschine ist ein Halbzoll-Schlauch.
The connection (device) of the machine is a half-inch hose.
But there is a third meaning of "Anschluß", which is "the act of making (or orchestrating, ...) a connection". For instance:
der Anschluß der Geschirrspülmaschine ...
could mean "the connection of the dish washer" or "the connection device of the dish-washer" but also "(the act of) connecting the dish-washer". This is a synonym for "das Anschließen", a substantiviertes Verb (verb made noun). Like in:
Der Anschluß der Geschirrspülmaschine war schwierig.
Connecting the dish-washer was difficult.
It is this third meaning which makes that word loaded: when Germany occupied Austria in 1938 their propaganda insinuated that - because of the language the two countries shared - Austria has always been part of Germany anyway and this would be not an occupation but merely putting together what always was one anyway. And for this they used the word "Anschluß".
I don't want to go into a historical analysis why this was utter nonsense (actually it was, but this here is not History.SE), suffice it to say that "der Anschluß" without giving any context - like "der Anschluß der Waschmaschine", "das Kabel für den Anschluß", etc., only "der Anschluß" - is often used for this act of occupation. Like many things related to the Nazis this is used only with caution and awareness of these historical implications. The only people (purposefully) acting like these implications would not exist are the ones wanting to redo the "thousand years" between 1932 and 1945.
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.
