Changes

Take the bus #27 from the centre the the final s top ''Platia Stavroupolis'' (Stavroupolis square). Then take bus #85 and you're already on your way. Almost any stop of this bus leaves you at a good hitchhiking point, but the nineteenth stop ''21o chiliometro'' (21st kilometre) is right on a petrol station on the way to Serres and the Bulgarian border (to Sandansky, Blagoevgrad, Sofia). The road is E79 and it's not a motorway, especially after the border. These city bus tickets cost only 50 cents (that you don't even have to pay) and take you quite some kilometres out of the city towards all destinations.

Basically you need to take 2 buses. Very similar to the above direction to Sofia. But this time it is bus #27 / #27a and bus #84 / # 84a. You can change buses in two different places.