[2] She received the nickname "Bobbie" as a junior player when, at a tournament, a representative of the South African Tennis Union remarked that the round shape of her face resembled that of an English policeman.

At the same tournament, she achieved her best Grand Slam singles performance by reaching the semifinals, which she lost in three sets to eventual winner Kea Bouman.

[5] In doubles, she and Bowder Peacock reached the final, but lost to the American couple Helen Wills and Elizabeth Ryan in straight sets.

[6] In 1929, on her second European trip, Heine won the singles title at the Irish Open, defeating compatriot Billie Tapscott in three sets.

In addition, she won the British Hard Court Championships, emerging victorious from a closely fought three-sets final against Joan Ridley that lasted two hours.

[12][13] Heine did not participate in the French Championships and lost in the fourth round of singles at Wimbledon, again to Wills, in a closely fought two-set match.

[5] In doubles, she teamed up with countrywoman Margaret Morphew to reach the semifinal, where eventual champions Sarah Fabyan and Alice Marble prevailed in two sets.