"Do you have a train ticket?"
Translation:Czy ty masz bilet na pociąg?
Firstly, Genitive is "pociągu".
Secondly... I guess I see your logic, but we don't use it this way. A ticket is "to something" or maybe "for something" in Polish (a ticket [to/for] a concert) and translates to "na + Acc". Or "do + a place in Genitive" (Kupiliśmy bilety do Rzymu = We bought tickets to Rome = We bought tickets for a plane/train/bus that will take us to Rome)
Besides, "bilety pociągu" (tickets of a train) would kinda sound as if the train owned the tickets ;)