She grew up as one of 10 siblings in St. Clair Shores, Michigan, outside Detroit. Her family name was Bachevich until she was 12, when their father, who had left Montenegro in 1916 during the upheaval of World War I, Americanized it. Two years later, they moved to Los Angeles. Bach graduated from UCLA and earned her medical degree there in 1966. She completed her residency at County-USC Medical Center and has worked as an assistant professor at UCLA.