After her family relocated to California, Bauer became the 1949 Southern Cal Amateur winner,[3] and posted other victories in the state.

By 1950, Bauer had played in the U.S. Women's Amateur three times, and had won an exhibition match against leading professional player Patty Berg.

[6] That season, she ended the LPGA Championship in a tie for sixth place, 10 strokes behind her sister, who won the tournament in a playoff.

[11] At the 1957 U.S. Women's Open, Bauer held a three-stroke lead halfway through the tournament, but finished in a tie for sixth after rounds of 87 and 79.

[14] In describing Bauer's swing, Marilynn Smith remarked that "her backswing made John Daly's look short.

[3] On March 8, 2023, the seven founding LPGA members not inducted to the World Golf Hall of Fame, which included Bauer, were jointly named to the Class of 2024.