She attended it for three years, then she was cast by dramatist Sabatino Lopez and she began performing together with the acting company headed by Enrico Reinach in Milan.

In 1930, Abba founded her own theatrical company and specialized in staging the works of Pirandello and other European playwrights like George Bernard Shaw, Gabriele d'Annunzio and Carlo Goldoni under the direction of prestigious directors like Max Reinhardt and Guido Salvini.

After her marriage, she performed summer stock at Cain Park Theatre in Cleveland Heights, Ohio in two productions: Divorçons by Sardou (August 21–24, 1941) and Pirandello's Right You Are (If You Say You Are) (July 22–25, 1942).

Abba was also a stickler for realism, insisting that Frank Monoco, a leading Cleveland restaurateur, play the maitre d'hotel so that he could serve an entire dinner onstage, which included the carving a whole fowl.

The total attendance for the 4 performances of Divorcons was 11,183 paid admissions, so Cain Park Theatre was eager to have Abba return in another production.

Dr. Dina Rees Evans, supervising director of Cain Park, recalled: "She wanted to have rehearsals longer than we were able to have them, many times four, five and seven-hour sessions.

She died, at 87, in Milan, from a cerebral haemorrhage, one day before her 88th birthday She published her autobiography in Italian, La mia vita di attrice.