Abbat worked at various times as a painter, illustrator, craftsperson, and teacher. She studied under James D. Smillie and R. Swain Gifford. Abbat studied at Cooper Union and the National Academy. She was a member of the American Watercolor Society. She was awarded a medal in an exhibition at the Massachusetts Charitable Mechanics Association in Boston and a prize at the San Antonio Expo.
When Abbat exhibited at the National Academy of Design in 1881, she lived at 337 4th Avenue, NYC. She also exhibited at the Boston Art Club. She painted flowers and landscapes in watercolor and oils. She was elected to the National Academy of Design in 1902.