Question: "What does the Bible say about women music ministers / worship leaders?"
Answer: Since the Bible really does not say much at all about music ministers, it is difficult to arrive at an explicitly biblical position on women music ministers / worship leaders. After the exodus, Miriam functioned in at least one instance as somewhat of a worship leader (Exodus 15:20-21). At the Tabernacle, male Levites seem to be the ones who led in worship (Numbers 8:25-26; 1 Chronicles 9:33). In Judges 5, Deborah and Barak led the Israelites in a song. Second Samuel 19:35 and Second Chronicles 35:25 mention “singing men and women” (see also Ecclesiastes 2:8).
David appointed men from among the Levites (1 Chronicles 15:16-24), who were skilled singers and used brass cymbals, harps, trumpets, and other instruments to accompany the singing. First Chronicles 5:12-13 gives a description of the Levites who led the music at the dedication of Solomon's temple, and they were all men. In the days of the rebuilding of the Temple, the sons of the Levites were appointed to lead the music in the Temple service (Ezra 3:10; Nehemiah 12:24). Psalm 68:25 says, "The singers went before, the players on instruments followed after; among them were the damsels playing with timbrels." The women were participating in, but not leading, the worship.
The New Testament contains no specific instructions or examples of how worship was, or should be, practiced in the Christian church. The New Testament nowhere speaks positively or negatively regarding female music ministers / worship leaders. Some point to 1 Timothy 2:12, that a woman is not to teach or take authority over a man, as a prohibition against women leading men in worship. However, this text is better understood as focusing on the pastoral role of shepherding/teaching than on other forms of leadership. Further, it is questionable whether leading worship involves any “authority” that would violate 1 Timothy 2:12. In what sense does a worship leader have authority over the worshippers? Could a woman lead with an instrument, but just not with her voice? Does not a woman playing piano/organ in some sense result in her “leading” the worship?
Generally speaking, it would seem that with the consistent pattern of male leadership in the church, it would be best for men to serve in the role of worship leader / music minister. At the same time, there is nothing explicit in Scripture that would forbid women from serving in the role. Many women are undeniably very gifted/skilled in worship, whether by voice or instrument. These gifts most definitely should not be ignored or neglected: “addressing one another in psalms and hymns and spiritual songs, singing and making melody to the Lord with your heart” (Ephesians 5:19 ESV).