2012 timetable for buses departing from Dubrovnik to Rijeka is available:

http://www.dubrovnik-online.net/english/transportation_coach.php

Daily departures from Dubrovnik at: 8,00 | 15,30 | 17.00

It is possible that the timetable for the Dubrovnik - Rijeka bus line during June and August will change, we will of course have the update as soon as it becomes available

More about travelling by bus: http://www.absolute-dubrovnik.com/dubrovnik-transport-information/category/travel-by-bus

See also: Location of Main Bus Station in Dubrovnik  http://www.absolute-dubrovnik.com/dubrovnik-transport-information/item/dubrovnik-main-bus-station?category_id=18