Following high school, she entered the Los Angeles Conservatory of Music to study with famed maestro Gaston Usigli.

She also sang with Dean Martin and Jerry Lewis in concerts at UCLA, and made numerous commercials for Lux Radio Theatre.

In 1958, Costa was called upon to substitute for Elisabeth Schwarzkopf at a gala concert in the Hollywood Bowl, conducted by Carmen Dragon.

[10][11] Costa went on to perform in 44 operatic roles on stages throughout the world, including Jules Massenet's Manon at the Metropolitan Opera, and Violetta in La traviata at the Royal Opera House in London and the Bolshoi in Moscow, and Cunegonde in the 1959 London premiere of Leonard Bernstein's Candide.

In 1961, for RCA, she recorded Musetta in La bohème, opposite Anna Moffo and Richard Tucker, with the Rome Opera House Orchestra and Chorus conducted by Erich Leinsdorf.

At the memorial concert, Costa sang "Libera Me" from Giuseppe Verdi's Requiem under the baton of conductor Zubin Mehta.

[14] Having retired from acting in 2014, Costa has dedicated her later years to inspiring children and teenagers, giving motivational talks at schools and colleges across the country.

[18] On November 10, 2014, she was awarded an Honorary Doctorate of Humane and Musical Letters from the College of Arts and Sciences, University of Tennessee, Knoxville.

[20] She also announced that she would no longer directly reply to fan-mail, but she would continue to sign autographs and meet fans at events while also focusing her efforts on working with young children.

[21] In August 2020 during the COVID-19 pandemic, Costa once again thanked fans for their continued support but also announced that she would no longer respond to any fan-mail at all due to the overwhelming amount she received following her 90th birthday.