Although most of her success was in women's doubles or mixed doubles, Whittingstall reached the singles final of the 1928 French Championships and the 1931 US Championships. She lost both of those finals in straight sets to Helen Wills Moody. She twice won the women's doubles title at the French Championships, in 1928 with Phoebe Holcroft Watson and in 1931 with Betty Nuthall. Whittingstall and Nuthall lost the 1932 final to the team of Moody and Elizabeth Ryan.
Whittingstall teamed with Ermyntrude Harvey to reach the 1928 women's doubles final at Wimbledon, losing to the team of Watson and Peggy Saunders 2–6, 3–6. She also teamed with Shoemaker to win the 1931 women's doubles title at the U.S. Championships, defeating Helen Jacobs and Dorothy Round Little in the final in two sets. Whittingstall twice partnered with Henri Cochet to win the mixed doubles title at the French Championships. In both 1928 and 1929, they defeated the team of Moody and Frank Hunter in the final. Whittingstall and Cochet lost the 1930 French final to the team of Bill Tilden and Cilly Aussem.
According to A. Wallis Myers of The Daily Telegraph and the Daily Mail, Whittingstall was ranked in the world top ten in 1928, 1929, 1931, and 1932, reaching a career high of World No. 3 in those rankings in 1931.
Bennett is credited with first wearing an above-the-knee form of divided skirt for competitive tennis.