Bach was born in Rosedale, Queens, and grew up in Jackson Heights, the daughter of Marjorie (1921–1997) and Howard I. Goldbach (1922–2001), a policeman. Her mother was Irish Catholic, while her father was Jewish (from a family from Germany, Austria, and Romania). She graduated from the all-girl Dominican Commercial High School in Jamaica, Queens, New York in 1964. A year later, in 1965, she shortened her name to Bach and began a highly successful career as a model posing for catalogs and fashion magazines. She is fluent in Italian and has a working knowledge of French and Spanish.