Does anyone have a link to timetables and fares for buses or trains between Sarajevo and Dubrovnik, and Sarajevo and Split in June 2014?
Bus: http://www.autobusni-kolodvor.com/en/terminal.aspx?k=173&d=070 (Zenica - Dubrovnik, Sarajevo - Split).
Train: Look like there are no trains to Dubrovnik.
There are no trains from Sarajevo to Dubrovnik. There are also no convenient train to Split. However, what you can do is take a train down to Ploce. This is a quite agreeable and scenic trip. The train leaves at 6:51, and arrives in Ploce at 10:58. Ploce is a regular stop on all Split - Dubrovnik and vv buses, so you should not have any trouble finding onward travel in either direction. The buses stop right outside Ploce station.
My experience with travel in this area is that there is more available than is shown on the internet. So inquire locally at the bus terminal and station.