Drysdale grew up on a sheep farm in Burgersdorp and the family had a tennis court as part of the property, where she practised with elder brothers Gordon and Jack Forbes, both tour players.

[1] As a 15-year old in 1955 she made a surprise run to the singles final of the Queen's Club Championships, a precursor tournament to Wimbledon.

She defeated two players who gained high seedings at Wimbledon, Darlene Hard and Dorothy Knode, but was unable to compete at the championships herself due to an age restriction.

[2][3] Drysdale's best performance at the Wimbledon Championships came in 1962 when she reached the fourth round of the singles and while partnering brother Gordon made the mixed doubles quarter-finals.

She had another tennis playing relation at this time in Valerie Koortzen, a Wimbledon quarter-finalist, who was her sister-in-law during her marriage to Gordon Forbes.