There are several direct trains daily to/from Bucharest international trains linking the Romanian capital with Sofia, Istanbul, Thessaloniki; they're rather slow at least 2 1/2 hours to get to Bucharest.
By bus
By bus
There are frequent buses from Bucharest at least one per hour, trip takes about slightly over one hour.There are also a few buses per day to/from Rousse, the Bulgarian city across the river coming and heading to Bucharest, but note they practically pass on the outskirts of Giurgiu.