Is there bus service available from Munich Airport to Vienna?
I highly doubt it. Eurolines has two buses/day (departures at 07:00 and 23:00) from Munich (city) to Vienna. You can take trains from the airport with as little as one connection (S-Bahn to Munich and a railjet from there to Vienna). See the German Rail site for detailed timetables and to book tickets. Enter Muenchen Flughafen Terminal 1 as your departure point and Wien as your arrival point.