Slovak literature is not widely translated into English, but a few titles will give context for a visit. Dominik Tatarka's The Demon of Conformity (1963) is a key work of Slovak dissident literature — a piercing satire of intellectual compromise under communism that made Tatarka a hero among Czech and Slovak writers. It is out of print in English but occasionally found in second-hand shops.
Michael Zantovsky's Havel: A Life (2014) is the most readable biography of Václav Havel, whose career intersected closely with Bratislava's history during the Prague Spring and the Velvet Revolution. Sharon Zukin's The Naked City (2010) is not about Bratislava but provides useful frameworks for thinking about how post-socialist cities have been transformed by tourism and gentrification.
For historical background, The Habsburg Empire by Martyn Rady (2020) covers the political world in which Bratislava operated for three centuries as the Hungarian capital. Highly readable and thorough.