Bulgarians are known for using a difficult alphabet (called Cyrillic after the name of one of its originators), but also for the fact that the most basic words in their language sound a bit too complicated. Yet, some of you might still be up for the challenge, and might want to be able to greet the Bulgarians they know in their native language.
Let me give you a short introduction to Bulgarian. Our word for “hello” is “здравей” pronounced “zdravey”. Alternatively you can use the Slavic "привет" pronounced "privet" like the bush.
For “thank you” in Bulgarian you can say “благодаря” pronounced “blagodaria”. Sounds too difficult? Well, the French “merci” also does the job, even if we spell it “мерси”.
The word for “cheers” is very similar to the words in other Slavic languages: “наздраве”, pronounced “nazdrave”. As in some other languages the word means "to one's health" and shares a root with the above "здравей".
Finally, our word for “goodbye” is “довиждане” pronounced “dovizhdane”. Yet, commonly Bulgarians use the Italian “ciao” spelled “чао”. Be careful, in contrast to Italians, we do not use “ciao” for “hello”, so greeting someone this way might cause serious confusions.
These words are a good starter set. By far not the simplest, but surely the most useful. Try learning them with Lexicum. Then look up these and other words you might consider potentially useful. At any later moment, when you find yourself with free time, you can flip through your word list as a way to memorise it.