Hi:
Maybe I have too much on the table but I really want to visit Sarajevo and Mostar. I want to take the train from Zagreb to Sarajevo which is quite long. However, I only want to take it one way. Flights out of Sarajevo are very expensive( even to Zagreb), Should I take the bus to Split? Or is there transportation to Serbia or Romania? I could go to Brasov, Belgrade, Budapest, or elsewhere if it is easy and affordable to get out of Sarajevo. Any suggestions? Thanks for your input.
Traveling east to west across the Balkans via ground transportation is a challenge. Two routes that I know work (because I took them in 2015) are:
Zagreb - Beograd - Timisoara (Romania)
Sofia - Nis (Serbia) - Podgorica (Montenegro)
I hate sitting up overnight on a bus (or train) so I didn't investigate overnight buses. Each of those trips took me two days, with the trip broken in the middle city.
I realize that those routings don't fit your needs, but I wanted to give you some idea about the time required to move around that part of Europe.
Skyscanner is a good place to look for flights.
To explore bus-vs.-train options, start with Rome2Rio. I've found the fares and durations provided by Rome2Rio to be quite inaccurate on many occasions and now use it primarily for high-level research on what modes of transportation might exist. If train service is revealed, go to the Deutsche Bahn website for schedule information. If a bus looks like it might be your best bet, keep drilling down on Rome2Rio until you find a link to the appropriate bus company's website or try Google: "Bus City A to City B".
What you're proposing to do will be an adventure. That's not a bad thing as long as your timeframe isn't too tight.
Other than backtracking, the only cross-border train that you might find running from Bosnia is between Mostar and Ploce, Croatia. Bus service to Split or Dubrovnik is more reliable in that direction. There's no train toward Serbia, but probably a bus.
You'll want to check if the train is actually running from Zagreb to Sarajevo. It was cancelled in December 2016 and looks like it might not be running yet: http://www.seat61.com/Bosnia.htm
It also shows that there might be train service form Sarajevo to Mostar, but you may want to check.
Buses or shuttles are the way to go to get around the Balkans.
The buses from Sarajevo to Mostar run regularly so it makes an easy day trip. Be careful purchasing round trip, if you decide to take a different bus on the return journey, you're ticket might not be valid as the bus may be run by a different company and you'll have to pay the one way fare on the return....not a huge concern because busses are super cheap.
If you don't want to fly out of Sarajevo, I would recommend a shuttle to Belgrade. I did the reverse and for 20 euros I rode a shuttle from Belgrade to Sarajevo and would recommend (door to door service) from Terra Travel. I emailed them and it seemed a little dodgy, but worked perfectly well.
Honestly, if you want to get to Romania from Sarajevo, I would bite the bullet and fly (search for a deal at skyscanner). Over land it just way too long of trip if you are not interested in seeing places along the way.