Iva studied music and drama at the Brno Conservatory, singing and violin. She was a member of the Na provázku Theatre, where she came to attention with the role of Eržika in the play Ballad for a Bandit. On the music scene, she has been active as a solo singer and violinist with her own songs composed to folk lyrics, but she has also performed with several bands.
In 2004, she performed at Carnegie Hall in New York in the role of Elvira in Mozart's opera Don Giovanni. She has two sons. With her younger son Antonín, she occasionally performs as the concert duo Bittová + Fajt Jr.