Well, I perfectly understand the people who make such jokes. :)
Most people know nothing about Bulgaria. Yeah, it's one of the communist countries, but it was not in the USSR, it's not Russia, we don't have nukes, we are not threatening to take-over the world... On the other hand, some people may have heard about corruption and that Bulgaria is poor. And when people hear poor, they do not imagine a place where people live in flats, have water supply, drive cars, ride buses and go to school, they imagine children playing in the dust and dying of hunger and spider-bites, with the closest hospital being in Solun (Thessaloniki) if they know that we are neighboring Greece and that Solun is in Greece.
It's just very easy to use Bulgaria as a generic country that can be anything for the Americans - a home for Islamic fundamentalists, home of the mafia, the place where the USSR used to store its nuclear waste, the place where the taxi-driver emigrated from, and really anything you can think of.
If they want to show something positive in Europe, they have what they need in Greece and Italy - ancient stuff, in Austria, Germany and Switzerland - medieval stuff, in France, UK, Germany - modern stuff.
If they want something truly ex-communist, they have the ex-USSR. If they want ethnic problems, they have Bosnia.
For everything else - there are Bulgaria and Romania. The latter, however, bears more rural associations.
Bulgarians also have these generic examples for different occasions - a Bulgarian generic village is Dolno Uino, a generic small town is Dolni Dabnik, a generic city would be Ruse (since very few Bulgarians have actually been there - it's not on the way to the sea). A generic communist place is Kazakhstan, a generic poor place is Zimbabwe, a generic Islam center is Afganistan, a generic place where there is nothing is Albania, a generic rich place is Germany, a generic very rich place is the USA, a generic place full of gypsies is Romania, a generic place full of drunk people is somewhere in Siberia...