"I am buying a bus ticket."
Translation:Kupuję bilet autobusowy.
While Polish usually has the adjective before the noun, there are lots of fixed names where it is the other way round. Let's have a few examples: ser żółty (yellow cheese), niedźwiedź polarny (polar bear), tygrys szablozębny (saber-toothed cat), wyraz bliskoznaczny (a synonym), Stolica Apostolska (The Holy See)... the examples can be from many different topics, although for example animals are one full of such situations. When the adjective is a word that simply describes the noun and it's your decision to add such information/opinion, the adjective should rather stand as first: mądry chłopiec (a smart boy), czerwony bilet (a red ticket).
Bilet autobusowy is fixed enough to exist in this form, and the other would seem very clumsy. You rather won't say bilet pociągowy (a ticket train), but bilet na pociąg (a ticket for a train - for a specific one). Similarly with planes. The fact that a bus ticket, when you mean the city transportation and not an intercity bus, is not for a specific bus, may also have something to do with it.
Do i have to use "autobusowy" in this case? Can I just put "autobus" in the genetive?
Don't think so, that would sound unnatural, like the ticket actually belongs to the bus :)
You could use "bilet na autobus", if it was a ticket for some intercity bus that you could for example buy online beforehand. A normal ticket for city transportation will be 'bilet autobusowy' - as it's the most common type of ticket you need, in many contexts you would simply use 'bilet'. (if you go to a kiosk and ask for a ticket, what else can it be if not city transport ticket?)
it is in accusative/biernik. Dative/celownik would be "autobusowemu".
adjective (autobusowy) has to match gender number and case with the noun it describes. "Bilet" is here in accusative (after kupuję), but as masculine not animated noun it has accusative=nominative.