Bus timetable Dubrovnik to Zurich, there is NO direct buses betweent the two cities, but travelling is possible via Split, below you can see timetable for buses from Split to Zurich. Check the info incos in the timetable to see operational days and period of the buses. From Dubrovnik there are very frequent buses to Split, you can see timetable here
If you are going on holiday in and has to return to Dubrovnik or to Split, you should buy a return ticket as this is cheaper then two single tickets