Salzman showed an early aptitude for the piano, and gave her first recital at the age of eight. The French pianist and teacher, Alfred Cortot, heard her play in 1932 while she was a student at Shulamit Conservatory and invited her to Paris to study. She graduated at the Ecole Normale de Musique then became a pupil of Magda Tagliaferro at the Conservatoire de Paris, where she was to win the Premier Prix de Piano in 1938, aged 16.
In 1963 she became the first Israeli to be invited to play in the USSR and in 1994, the first Israeli pianist invited to play in China. Besides performing as a soloist, she was a member of the Israel Piano Quartet.
She was a Professor and the head of the piano department at Tel Aviv University and served on the jury of many piano competitions, including the Arthur Rubinstein, Vladimir Horowitz and Marguerite Long competitions. She taught piano to many students, including Dror Elimelech, Nimrod David Pfeffer, Elisha Abas, Iddo Bar-Shai and Yossi Reshef.