Bogaevskaya was born October 25, 1915, in Petrograd in the family of scientist, archaeologist, and art historian. She studied at the Art and Industry College, where she was a student of Dmitry Zagoskin (1931–1932). Then continued education in the Leningrad Institute of Painting, Sculpture and Architecture, where she was a student of Sergei Priselkov, Genrikh Pavlovsky, David Bernshtein, and Alexander Osmerkin (1933–1940). In 1940 Bogaevskaya graduated from the Institute of Painting, Sculpture and Architecture in Alexander Osmerkin workshop with the rank of artist of painting. Her degree work was the painting "Meting of girlfriend".

In 1940 Bogaevskaya married a fellow student at the institute artist Gleb Savinov. In 1940–1941, she taught painting at the Secondary Art School at the Leningrad Institute of Painting, Sculpture and Architecture. Bogaevskaya was a regular participant of exhibitions of Leningrad artists since the late 1940s. She was a talented colorist. The leading theme of her work - child portrait, still life in the interior and exterior. Since 1940 Bogaevskaya was a member of the Leningrad Union of Soviet Artists. Works of 1950–1960s nominated her of the leading painters of Leningrad.