It would be hard to deny that there was such a bias in the composition of orchestras. As late as 1970, the top five orchestras in the U.S. had fewer than 5% women. It wasn't until 1980 that any of these top orchestras had 10% female musicians. But by 1997 they were up to 25% and today some of them are well into the 30s. What is the source of this change? Have they added jobs? Have they focused on work that appeals to women?
The size of a major orchestra is quite stable; they all have around 100 musicians. Furthermore, the types of jobs do not change. The increase in the number of women cannot be attributed to a redistribution giving the orchestra fewer bassists traditionally played by men and more harpists where more women are found.
In the 1970s and 1980s, orchestras began using blind auditions. Candidates are situated on a stage behind a screen to play for a jury that cannot see them. In some orchestras, blind auditions are used just for the preliminary selection while others use it all the way to the end, until a hiring decision is made.
Even when the screen is only used for the preliminary round, it has a powerful impact; researchers have determined that this step alone makes it 50% more likely that a woman will advance to the finals. And the screen has also been demonstrated to be the source of a surge in the number of women being offered positions.
https://www.theguardian.com/women-in-leadership/2013/oct/14/blind-auditions-orchestras-gender-bias