You could always buy a card - 50 levs for one month for all public transportation including the metro. In this way you don't have to bother about buying tickets, validating them and so on...
You may also buy a cheaper card for only one line (the bus line) - you may still use it with other bus lines that have the same route and stop on the same bus stops. Or you could buy one for two lines (that is, the metro and the bus line). Plenty of choices there. The bureaus that sell / issue the cards work on weekends. There is one in the Serdica metrostation. Just take one of your Bulgarian friends to help you a little bit with translation. That's better than being constantly exposed to the risk of being caught in the bus without a ticket and all of its consequences.
There are also cards for three months period.