Born in the Soviet Union in what is now Moldavia, Bertini emigrated to Israel as a young man and studied in Milan and in Paris with Arthur Honegger and Olivier Messiaen. He founded the Israeli Chamber Orchestra in 1965, and led that ensemble until 1975.
Later, he served as chief conductor of the Jerusalem Symphony, music advisor of the Detroit Symphony, principal conductor of the Cologne Radio Symphony, general music director of Frankfurt Opera, music and artistic director of New Israeli Opera, and music director of the Tokyo Metropolitan Symphony. He was music director of Naples' Teatro di San Carlo at the time of his death.
Among Bertini's recordings were a cycle of Mahler symphonies for EMI.