Travelling by direct bus from Dubrovnik to Vienna is not possible, nevertheless it doing the trip by bus is for sure possible, what you have to do is first to take a bus from Dubrovnik to Zagreb, from Zagreb you then have several daily bus departure to Vienna. Here you can see timetable Zagreb to Vienna.
Train: As there is no train to and from Dubrovnik, train is not an option.
Plane: During summer season, their might be options to travel by plane
Car: Travelling by car from Dubrovnik to Vienna takes about 9-10 hours, some car rental companies offer one way rental to Vienna for an additional fee.