Bach was born in Cleveland, Ohio, the daughter of Norma Jean Kucera (née Verdugo), an acupuncturist, and Bernard Bachman, a rancher. Her mother was of Mexican descent and her father was of German ancestry. She is descended from the Verdugo family, one of California's earliest landed families. She grew up on a ranch in South Dakota, where she visited her grandparents in Faith. In 1970, Bach graduated from Stevens High School in Rapid City, South Dakota and briefly studied drama as a major at UCLA where she supplemented her income by making clothes for friends and theatre groups.