Her family settled in Herzliya. Her mother was a piano teacher. Miriam first took up piano lessons but when she was eight years old she made a definite choice for the violin. Her studies in Tel Aviv with Alice Fenyves continued under her brother Lorand Fenyves at Geneva, Josef Gingold at Indiana University, and Ivan Galamian at the Juilliard School.
She has been Artistic Director and chair of the faculty at the Steans Institute for Young Artists of the Ravinia Festival since 1993. She was a member of the Mendelssohn String Quartet. She is a member of the faculty of the New England Conservatory. She was Professor of Violin at the Jacobs School of Music at Indiana University. Her students include Pekka Kuusisto and Nancy Zhou.
She gives master classes internationally.
She is married to the violinist and violist Paul Biss, the son of the Russian-born cellist Raya Garbousova. Their sons are the pianist Jonathan Biss, with whom she often plays, and Illinois State Senator Daniel Biss.