This is a tough question. First we need to understand the restrictions which the Bible teaches regarding men and women. 1 Corinthians 14:34-35 commands a woman to be silent “in the church” (referring to the assembly of the local church) but 1 Timothy 2:12-13 commands (in general conduct): “Let a woman quietly receive instruction with entire submissiveness. But I do not allow a woman to teach or exercise authority over a man, but to remain quiet” (NASB). The example in Acts 18:26 makes it clear that this does not prohibit a woman from discussing spiritual matters in a man’s presence (or even helping him understand the truth). But the attitude must be one of humble submission, not dominance or authority. I believe these principles allow men and women to discuss the Bible in classes that do not constitute the church assembled, while in the assembly of the church a woman must be silent (with the exception of singing, or confession of Christ).
When it comes to prayers, there are some things which Scripture addresses and some which it does not. For example, while Jesus rebukes prayer to be seen by men (Matt. 6:5-7), this does not prohibit public prayers that can be heard by others (see Acts 4:21-34; 1 Cor. 14:13-16). We have come to describe this as “leading prayer” but I can find no Scripture which speaks of it in this way. Properly, I may hear someone else pray, but only I can pray for myself. No one can “lead” me in prayer—they can only offer thoughts which I must echo in my own prayer. Even so, voicing a public prayer is generally viewed as a type of leadership. Because of this, certain precautions must be applied. In the assembly of the church, a woman is prohibited from voicing a public prayer by 1 Corinthians 14:34-35. Further, even in a Bible class which does not involve the church assembled, if a woman voices the public prayer for a class of men and women this would clearly seem to be exercising "authority over a man” (1 Tim. 2:12-13). That leads to the question of more private times when a man and a woman are together. Is it a violation of 1 Timothy 2:12-13 for a woman (in full submission to her husband) to voice a prayer within his hearing? Some would say this would be “leading” the prayer, and thus “exercising authority.” Others would contend that if this is done with the permission of her husband it is no different from the example of Acts 18:26. Unfortunately, Scripture has not spoken regarding the specifics of this question, so it must be left to personal judgment and conscience (under the dictates of the principles that have been revealed).
If the situation is that of a “spiritual woman” with a man who is not spiritual, that adds to the complication. Are we talking about a Christian woman and a non-Christian? Are we talking about those who are married or just dating? Whatever the case, such a woman will have to reach a judgment (with the man in question) regarding these issues. If she feels that it would be wrong to voice her prayer out loud, there is nothing wrong with bowing her head in a silent prayer (cf. 1 Sam. 1:13). If she is seeking to influence the man, she must make certain that her action is not perceived as “exercising authority” over him. We lose influence if we act in ways that unbelievers see as hypocritical. If a Christian woman is put in the difficult position of being the only spiritual influence over her children, certainly she must do all that she can to set a godly example. Some of this can take place with the children alone. At times when she is in the presence of the man, again, she needs to reach a judgment which will not seem hypocritical to the man or her children.
Difficulties such as this reinforce how important it is for Christians to establish relationships with Christians. When this does not happen, how easy it is for a Christian to find herself “unequally yoked together” with an unbeliever (2 Cor. 6:14).
Kyle Pope, August 2010