Bach was born in Warren, 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, South Dakota, and graduated from Stevens High School (1970) in Rapid City, South Dakota. She studied arts at UCLA where she supplemented her income by making clothes for friends and theatre groups.