Bohuslav was the younger brother of Oskar Kokoschka (1886-1980), with whom he had a close relationship. Their father came from a goldsmithing family in Prague, their mother from Austria. The family was extremely poor.

Bohuslav's work was included in the Der Regenbogen (the rainbow) exhibit in 1920 at the Haus der Jungen Künstlerschaft (House of Young Artists) in Vienna, along with that of Anton Faistauer (1887-1930) and Paris von Gütersloh (1887-1973). An edition of 500 copies of four original lithographs, illistrations to "Der schöne Garten" (the beautiful garden), a fairytale by Emil Alphons Reinhardt (1889-1945), was published in 1920. Kokoschka wrote expressionist poetry as well as a novel, "Ketten in das Meer" (chain into the ocean), which was not published during his lifetime.