Bulgarians speak Bulgarian (what else!). Bulgarian is a Slavic language related to Russian, Serbo-Croatian, Czech and Polish. It is written in the Cyrillic alphabet, which is most familiarly used by the Russians. It is a phonetic language, which means that each letter in a word has its own sound. Once you master the alphabet you can read.
Bulgarian is by far the easiest of the Slavic languages to learn. The Bulgarians long ago abandoned the case system, and sentence structure is very similar to that of English. Don't be intimidated or afraid as you learn the language. It's hard, but with effort and study everyone learns it.