Hess studied at the Guildhall School of Music and at the Royal Academy of Music under Tobias Matthay. She made her concert debut in London in 1907 and in the United States in 1922. From 1939 to 1946, even during the height of the German bombardment of London, she organized and frequently performed at daily concerts at the National Gallery to bolster the morale of Londoners.

In her earlier years she cultivated an intimate chamber music style that was particularly effective in her performances of the works of Schumann. The more powerful style of her later career became evident in her performances of the concerti of Beethoven and Johannes Brahms. She was made Dame Commander of the British Empire in 1941.