Arbegast graduated form Oberlin college in 1945, and earned an M.S. degree in Ornamental Horticulture from Cornell University in 1949 as well as a M.S. in Landscape Architecture from Berkeley in 1953.She taught both full and part time at Berkeley in the Department of Landscape Architecture from 1953 to 1967. During that time she maintained a part time professional practice. In 1967, she gave up teaching and began a full time professional practice that continued through 2003. Arbegast was involved in the design of large scale residential gardens/estates, wineries, in addition to commercial, educational and public projects. In addition to her professional practice, Arbegast has been a member and trustee of many boards and foundations. Arbegast played a key role in the gift of the Blake Garden to the UCBerkeley Department of Landscape Architecture and the transfer of Filoli Gardens to the National Trust. She was largely responsible for the donation of the Beatrix Farrand Collection and Gertrude Jekyll Collection as well as the Farrand scholarship and fellowship funds to the UCBerkeley Department of Landscape Architecture.