Bakst was a descendant of the Russian artist Léon Bakst. His teachers were initially his mother and pianist Józef Turczyński, then Abram Lufer (who had won 4th Prize at the 1932 Chopin International Piano Competition) and later Konstantin Igumnov and Heinrich Neuhaus at the Moscow Conservatory, and finally with pianist Zbigniew Drzewiecki.
Bakst was a prize winner at the 4th Chopin International Piano Competition in Warsaw in 1949 and performed in Europe and the United States the Far East and numerous other places around the world. He was particularly known for his interpretations of Chopin but also played composers as diverse as Aaron Copland and Juliusz Zarębski.
He immigrated to Great Britain in 1968 and did not return to his beloved Poland until 1988 when he was feted in a televised concert at the Warsaw Philharmonic Hall.
Among the most gifted students he taught, according to Bakst himself, are Andrew Wilde and Pawel Skrzypek, and, for her complete Bach performances, Jill Crossland. Others whom Bakst held in high regard are Alicja Fiderkiewicz, Janusz Olejniczak and Ronan O'Hora, whilst the long list of other students includes the highly successful Paul Lewis as well as Marta Karbownicka, Graham Scott, Mark Anderson, Matthew Schellhorn, Peter Seivewright, Timothy Horton and many others. He also gave lessons to popular music artists, such as Don Airey of Deep Purple.
During lessons he could be so inspired and inspiring, but also had a reputation as a highly disciplined and strict task-master often making enormous demands on the most gifted students. His attention to sound (Artur Rubinstein was frequently mentioned) was legendary and any deviations from the text would be immediately picked up.