Heather Bills was born in Adelaide, South Australia and came to the UK to take up studies at the Royal College of Music in London, studying with Christopher Bunting & Amaryllis Fleming, during which time she won the Australia Prize of the Royal Overseas League Competition. She attended various chamber music courses, receiving coaching from such artists as Jacqueline du Pre, William Pleeth, Emanuel Hurwitz and the Beaux Arts Trio.
In 1983 she became the Co-principal Cellist of the Halle Orchestra in Manchester, staying until 1991 when she moved to Anglesey, North Wales, became a member of the chamber group Ensemble Cymru and principal cellist of the Welsh Chamber Orchestra. In 2008 she returned to Manchester, where she continues to freelance with the Camerata, Halle and Northern Chamber Orchestras.
With her husband, the pianist Harvey Davies, she is a founder member of the chamber group the “Pleyel Ensemble”.