Betty studied life drawing and sculpture at the High School of Commerce under Lionel and Ernest Fosbery. She danced and acted with the Ottawa Little Theatre, through the 1930s and 1940s when she was also frequently photographed by Yousuf Karsh. She held her first solo exhibition in the theatre's foyer in 1945. In the 1960s, Davison took art classes at Carleton University and the Ottawa Municipal Art Centre, and credited Alma Duncan with encouraging her to return to her artistic career. Further studies in printmaking with Hilde Schreier during the 1970s led Davison to experiment with the creation of cast paper reliefs, and it is in this medium that she found success. Her 1974 print Paper Roses received a $1,000 award from the Ontario Arts Council. She received the Martha Jackson Gallery purchase award in 1977; the Harold Pitman prize in 1978; and a purchase award from the Art Gallery of Brant in 1983. Davison died in Ottawa.