Born and raised in the Bronx, New York, she decided to pursue a career as a singer when she was still a child; she was encouraged by her mother, a concert singer, and by her music teacher at Walton High School, who arranged for her to audition for a scholarship at the Juilliard School. Bigley won the scholarship and attended Juilliard, later studying at the Royal Academy of Dramatic Art in London.
In 1946, she joined the chorus of Rodgers and Hammerstein's Oklahoma!, which had opened in 1943. After five months, Bigley was transferred to the London production and soon took over the role of Laurey opposite the Curly of Howard Keel (then billed as Harold Keel). She remained in that production for more than three years, later performing in Gay Rosalinda, the first television musical ever produced by the BBC. Bigley also starred in Café Continental, a weekly TV show filmed in London and broadcast in the U.S., and performed an acclaimed nightclub act titled Bagatelle.
In the wake of her successes in London, Howard Hughes -- then the owner of RKO Pictures -- brought Bigley back to America for a screen test. Around that same time, however, she was cast as Sarah Brown in Guys and Dolls. The show co-starred Robert Alda, Vivian Blaine, and Sam Levene; it opened in 1950 and became an enormous hit. In 1951, Bigley won a Tony Ward for her performance in the Best Featured Actress category.
Her only other Broadway credit was Rodgers and Hammerstein's Me and Juliet, which opened in 1953 and had a relatively short run of 358 performances. Bigley played the role of Jeanie; her co-stars included Bill Hayes and Ray Walston. During the '50s, Bigley was a frequent presence on television, appearing often on The Ed Sullivan Show and other variety programs.
She met Lawrence Barnett, then president of the talent agency MCA, while she was starring in Me and Juliet. They soon married, and Bigley retired from show business in 1958 to raise her children; the family lived in Rye, New York for 30 years. The Barnetts were known for their philanthropic endeavors, and Bigley donated her theater memorabilia to the Jerome Lawrence and Robert E. Lee Theatre Research Institute at Ohio State.
During the final years of her life, Bigley lived with her husband in Rancho Mirage, California. In 2000, she was elected to the board of trustees of the McCallum Theatre in Palm Desert; last year, she became the first woman chair of the theater's board. The Barnetts were also heavily involved with the ALS Association, a national organization dedicated to finding the cause of and the cure for amyotrophic lateral sclerosis (also known as "Lou Gehrig's Disease").
Bigley is survived by her husband, six children, 16 grandchildren, and four great-grandchildren.