American financier, the first woman to head a member firm of the New York Stock Exchange.

Josephine Perfect grew up in Brooklyn, New York. After graduating from Brooklyn Heights Seminary and attending Colorado College from 1918 to 1919, she became active in various civic groups in Brooklyn, notably the Junior League. With her sister she also operated a successful Christmas card business. In August 1942 she married Charles U. Bay, a senior partner in the brokerage firm of A.M. Kidder & Co. She took an active interest in his business. During 1946–53 she accompanied her husband to Norway, where he served as U.S. ambassador. While there she worked to help relief efforts in the war-torn country.

In 1955, when Charles Bay fell ill, Josephine Bay was elected to a limited partnership in A.M. Kidder. When he died in December of that year, she succeeded him as a director of American Export Lines, a passenger and shipping firm then with gross annual receipts of $60 million. In 1956 she was chosen chairman of the executive committee of American Export Lines. In December 1956 she was elected to the presidency and chairmanship of the board of A.M. Kidder.

In February 1959 she became chairman of the board of American Export Lines, a post she held until the next year. She remained at the head of A.M. Kidder until her death.