In Romania drivers often expect some payment for a ride. It is still cheaper than trains and buses though.
Bucharest (Romanian: Bucureşti) is the capital of Romania.
Heading west to Sibiu, Serbia, Belgrade: Get the metro to Paci (note the metro is a bit crazy - if you're not careful the trains change lines without warning and you can end up at Gara De Nord again!).
From Paci find the main road going west, and go to the first bus stop. Get the first bus that says Carrefour and go all the way to Carrefour shopping centre, this is the start of the motorway. Theres a part where the fence is broken and you can access the motorway here - it's actually a very good spot to hitch, since traffic coming from the big shopping centre stops here.