Travel by Car: The driving distance between Mostar and Tuzla is about 240 km, which equals a travel time of about 4 hours.
Travel by Bus: Timetable, if any, for direct buses between Mostar and Tuzla can see here, if there are no direct buses available it is possible to from Mostar to Sarajevo where you then switch to a bus to Tuzla. Timetable and prices for buses from Sarajevo to Tuzla, you can check here.
Alternative ways of travelling from Mostar to Tuzla:
Travel by train: There is train connection between Mostar and Tuzla, more information you can check here.
Travel by plane: On this route there is no direct flight.
Map with buses from Mostar: