1

There are no trains and there is no bus to the best of my knowledge that passes in the direction you want. It is possible to make this trip but expect to spend a day in transit. You will need to take a bus from Zabljak to Niksic and then another from Niksic to Sarajevo.

Unfortunately, I can't find the bus schedules for these routes online.

Ruth

2

There are two or three morning buses from Sarajevo Lukavica to Podgorica via Niksic, so this should also be the case the other way around.

3

QUOTATION FROM ANOTHER FORUM
Maybe the best way to get to Žabljak, especially for those unfamiliar with roads in northern Montenegro, which are not up to European standard. As of early April 2011, the Žabljak bus station posted the following schedule:

Podgorica-Niksic-Žabljak: 05:55-07:00-09:15; 13:50-15:00-17:30; 15:57-17:20-19:40

Niksic-Žabljak: 07:00-09:15; 10:00-12:15; 10:05-13:10; 15:00-17:30; 16:20-19:40; 18:00-20:15

Pljevlja-Žabljak: 06:45-08:50; 08:00-09:15; 10:00-11:25; 11:20-12:30; 14:55-16:25; 15:15-16:30

Belgrade-Žabljak: 23:30-08:50

Sombor-Novi Sad-Belgrade-Žabljak: 04:45-06:30-08:00-16:00

And leaving Žabljak:

Žabljak-Niksic-Podgorica: 11:25-13:50-14:30; 12:45-15:00-15:50; 18:00-20:20-21:15

Žabljak-Niksic: 07:15-09:35; 16:10-18:20; 16:25-18:25

Žabljak-Pljevlja: 09:30-10:45; 11:00-12:20; 13:10-14:25; 14:00-16:00; 19:25-20:40

Žabljak-Belgrade: 14:00-23:30

Žabljak-Belgrade-Novi Sad-Sombor: 11:00-20:00-21:20-23:10

END OF QUOTATION.

My notice:
Next to NP Durmitor in Zabljak - Montenegro is Tara NP which is in Serbia. Very close accross River Drina is NP Sutjeska (Foca town) in Bosnia and Herzegovina B&H entity Republika Srpska. The most atractive is Djurdjevica Tara Bridge which is in Montenegro:
Djurdjevica Tara Bridge looks like part of nature.