Buckley was born in Fort Worth, Texas to Ernest Buckley (who was born in South Dakota) and Betty Bob; she has four siblings, of whom she is the eldest.

She attended Texas Christian University as a journalism major and was crowned "Miss Fort Worth" in 1966 and was runner-up in the Miss Texas competition.

Buckley made her Broadway debut in 1969 and has been called "The voice of Broadway!" by New York Magazine. Even extremely difficult to please critic John Simon had nothing but good things to say about her.

On Broadway, she has appeared in:

1776 - 1969, her Broadway debut as Martha Jefferson where she sang "He Plays the Violin." Cats - 1982 where she won the Tony Award for outstanding achievement in the theatre that year for playing Grizzabella. The Mystery of Edwin Drood - 1985 Carrie - 1988 - as Carrie's mother Sunset Boulevard - 1994 (Andrew Lloyd Webber's adaptation of the film) as Norma Desmond, the aging diva silent screen actress. Triumph of Love - 1997 with F. Murray Abraham and Christopher Sieber She is perhaps best known for the 1977 - 1981 TV dramedy Eight is Enough. She joined the show in its second season after the original star, Diana Hyland, died after the first four episodes of season one. Hyland's character (Joan Bradford) died, and Buckley was cast as Sandra Sue Abbott (nicknamed Abby), who went on to become step-mother to the 'eight' (kids) the series' title refers to.

Buckley also gave a much remembered performance in the original movie version of Carrie in 1976. She played Miss Collins, Carrie's gym teacher.

Buckley currently lives on a ranch in Parker County, Texas where she was the producer of the PBS series Wishbone, and participates in NCHA cutting horse competitions.