Travel by Car: The driving distance between Cologne and Mostar following fastest route is 1.580 km, and estimated travelling time is around 14 hours and 30 minutes. Recommended route goes via highway in Croatia, Slovenia and Austria where tool fees apply. The route also goes via highway in Germany, but it is free of charge.
Travel by Bus: Timetable and price tickets for buses from Cologne to Mostar, if any, you can find here. Other alternative is to travel with bus from Cologne to Mostar via Sarajevo or Split in Croatia.
Alternative ways of travelling from Cologne to Mostar:
Travel by train: From Mostar there is a possibility to travel by train to Zagreb (via Sarajevo), and then continue with international train to Gremany. Travelling by train in Bosnia and Herzegovina and Croatia is relatively slow, so travelling time in total is much longer compared to travel by bus or car.
Travel by plane: There is no direct flight, but there is option to fly from Split to Cologne in Germany. Low cost company Germanwings have whole year flights from Cologne to Split and other way around.
Map with buses from Mostar: