City Transport with the small vans is best and cheapest way to have a transport in Bijeljina. Ticket for the City drive coasts 0,5 Convertible Mark (1,95 KM = 1 Euro) and for villages 1 KM. There are timetables at every bus station.
For a western Europe tourists, the best way to reach Bijeljina is to turn right (coming from Croatian border) to Kuzmin. The border between Serbia and Srpska i 20 km far from the highway. You have 25 km more to Bijeljina.
This is a scene from the Serbian-Republic Of Srpska border.I know it seems a "little" crowdy,but it is not.The cars have advantage so you can cross the border in less then 5 minutes.