Born in Munich, Beibl appeared as a child at the Bavarian State Opera, where she received training as a dancer.
Her musical career began as an operetta soubrette at the Stadttheater Fürth, to which she belonged from 1934 to 1938.
In the 1950s and 1960s she was a highly acclaimed star at the aforementioned theatre, where she played alongside Harry Friedauer, Rosl Schwaiger, Dorothea Chryst, Ferry Gruber, Martha Kunig-Rinach and others and belonged to the permanent ensemble until 1978.
She played among other roles Annamirl in the first film adaptation of Die drei Dorfheiligen [de],[1] and the landlady Neudecker in Der Hochzeitslader of the TV series Königlich Bayerisches Amtsgericht.
Biebl was married three times, including to the operetta singer Hans-Heinz Bollmann and Ernst von Klipstein, whom she met during the shooting of Die drei Dorfheiligen.