In 1967 Bakočević made her debut at the Teatro Lirico Giuseppe Verdi in Triest the role of Olga in Nikolai Rimsky-Korsakov's The Maid of Pskov.
That same year she joined the roster at the Vienna State Opera where she sang regularly through 1982 in such roles as Minnie in Puccini's La fanciulla del West, Elisabetta in Giuseppe Verdi's Don Carlos and Maddalena in Umberto Giordano's Andrea Chénier among many others.
She joined the Metropolitan Opera in New York City for the 1968–1969 season, singing there Cio-Cio-San in Madama Butterfly, Leonora, Marguerite in Faust, Micaela in Carmen and Mimì.
In 1973 she made her debut with the Philadelphia Lyric Opera Company as Amelia in Un ballo in maschera with Plácido Domingo and Bernabé Martí alternating as Riccardo, Cornell MacNeil as Renato, Lili Chookasian as Ulrica and Patricia Wise as Oscar.
She sang three roles in French; Giulietta in Jacques Offenbach's Les Contes d'Hoffmann, Marguerite in Charles Gounod's Faust and Micaela in Georges Bizet's Carmen.