In 1976, Bibby returned to New Zealand to take up a two year Mozart Fellowship at the University of Otago in Dunedin.[4]
Bibby relocated to Wellington in 1978 and worked as a pianist, composer, music teacher and university lecturer.[5][6]
Bibby was active in several music-related organisations, serving as president and chair, and founded the CHAMPS Trust to offer opportunities for youth in music. She was awarded the Philip Neill prize in composition, the Kranichsteiner prize in composition and the Darmstadt prize for new music.[7]