Under the Yoke by Ivan Vazov (1893) is the founding Bulgarian novel — the story of the failed April Uprising of 1876 against the Ottomans, told from a small Balkan town. Required reading in every Bulgarian school. The English translation is readable and the historical scope explains much of why modern Bulgaria feels the way it does.
Street Without a Name by Kapka Kassabova is a memoir of growing up in Sofia in the 1980s, the family's emigration to New Zealand after 1989, and her returns as an adult. The chapters on Sofia under socialism — block apartments, food queues, summer trips to the Black Sea — are the best portrait of late-Communist Bulgarian life in English.
Border by Kapka Kassabova is set further out, on the Bulgarian border with Greece and Turkey, but it gives the Balkan context Sofia sits in. Her writing on the Rhodope mountains and the legacy of population exchanges is unmatched.
Wild Bulgaria by Janet Wolff is a practical traveller's account of long walks in the Rila and Pirin mountains south of Sofia, useful if you plan to leave the city for the highlands.
Wolves at the Door by Stefan Bachmann is a more recent novel set partly in Sofia during the late Communist transition — useful for the textures of 1990s Bulgarian life.