Bunty’s father Fred was club professional at Bootle Golf Club. She initially faced discrimination from golf administrators because of his working-class occupation, how times have changed. In 1955 she married Roy Smith, a Scottish Airlines pilot who was tragically killed in a 1957 crash. They had one daughter and Bunty curtailed her playing career to raise her.  She then became active in golf administration and developing junior golf. She was made OBE for "services to Ladies Golf" in the 1977 New Year Honours a year before her death. The OBE medal is currently on loan from the Club to the Liverpool Museum as part of their homage to sportsmen and women who helped shape the sport(s) we know today.

Bunty’s home club was Royal Birkdale. She won the British Ladies Amateur in 1949 and 1954 and was runner-up in 1951 and 1952. She played in all six Curtis Cups from 1950 to 1960, and was non-playing captain of the Great Britain and Ireland team  in 1962 and 1972. Her final-hole victories over Polly Riley in the 1956 and 1958 tournaments secured a win and a draw respectively for the British team, the first time it retained the cup. In the United States she was "hardly known", though she finished tied for 6th in the 1949 U.S. Women's Open. She was also a non-playing captain of the British team in the Vagliano Trophy a feat that has been emulated in recent years by another Royal Birkdale Member, Janet Melville.

Herbert Warren Wind called Bunty a "slight, quiet, entirely undramatic girl" and an outstanding clutch player. Enid Wilson said she had "a very frail physique but the temperament of a tigress" Her swing had a pronounced hiatus at the top which Henry Cotton described as "one of the prettiest swings in the game".

The Club ha played the Bunty Stephens Mixed Foursomes for many years and in the late 1980's, Club Members John & Nancy Benstead  donated the trophy.