And it shall come to pass afterward, that I will pour out my Spirit on all flesh; your sons and your daughters shall prophesy, your old men shall dream dreams, and your young men shall see visions. Joel 2 v 28
On the next day we departed and came to Caesarea, and we entered the house of Philip the evangelist, who was one of the seven, and stayed with him. He had four unmarried daughters, who prophesied. Acts 21 v 8 – 9
This is to “prophesy”, which we generally take to mean “predicting the future”. While this was something prophets did (cp. Duet 13:1-5), the definition of a prophet was someone that speaks the words of God.
Lest we conclude that this was only a special thing at the hand of God, Paul tells Titus:
Older women likewise are to be reverent in behavior, not slanderers or slaves to much wine. They are to teach what is good, and so train the young women to love their husbands and children (Titus 2v3-4)
What is teaching what is good but teaching about the Bible?
But there are some caveats:
Every man who prays or prophesies with his head covered dishonors his head, but every wife who prays or prophesies with her head uncovered dishonors her head, since it is the same as if her head were shaven. (1 Cor 11v4-5)
This is a controversial passage – there are several ways to read it and understand it, but it is certainly allowing for women to prophesy. Paul gave another restriction to Timothy:
I do not permit a woman to teach or to exercise authority over a man; rather, she is to remain quiet. (1 Tim 2 v 12)
Again, the precise meaning of this is controversial, and some have taken it to mean that women should not teach the Bible at all. But considering the other passages above, it’s clear that this isn’t how we should understand it; instead the focus is on authority: women should not acquire authority by teaching the Bible.
So women can teach the Bible, providing some limits are observed.