Durankulak-Vama Veche border crossing
The Durankulak-Vama Veche border crossing is a border crossing between Romania and Bulgaria, a few kilometres away from the Bulgarian town of Durankulak and the Romanian Vama Veche. Usually car traffic is low through this border, so it's not easy to catch a ride. Also, it is said there is some drug traffic between, so drivers are cautious. Be prepared to wait long.
The best possible thing to do is to walk from Vama Veche to the border and ask car drivers when they stop for document check. Regular bus from Romania to Bulgaria goes twice a day through the border. No bus stops on Bulgarian side.
Update (June 2015). Marion_and_John walked from Vama Veche to the border (less than 2km). On the Bulgarian side, there is a very large area where you can hitch, lots of space for cars to stop. Main issue is lack of traffic. Got a lift to Varna in 1h30'.