Dear Beloved, for the purpose of this discussion, please set aside our traditions and let us critically consider this question using only the scriptures as our tool to answer this question. Traditions are good but if we are overly taken by them, they can make the word of God of non-effect in our lives and reasoning. Let us begin.
It is always intriguing for me that when this subject comes up and I see people quoting, “…he that finds a wife finds a good thing…”(Pro 18:22) and they use this as justification that it is the man that has to do the proposal. That scripture does not say “he that finds a wife does the proposing”. It does not say a man must do the proposing. Those from cultures where males predominantly propose are more disposed with going with this verse whereas those from cultures where females do the proposal like in Orango Island (Guinea-Bissau) and certain Indian casts may go with scriptures like:
Jer 31:22 How long will you waver and hesitate [to return], O you backsliding daughter? For the Lord has created a new thing in the land [of Israel]: a female shall compass (woo, win, and protect) a man. AMPLIFIED BIBLE
This is the new thing God did in Israel. But here also it does not say a woman does the proposing only that she woos or wins the man. In a different scenario, Jesus’ great grandmother Ruth said the following:
Rth 3:9 (9) And he said, Who are you? And she answered, I am Ruth your maidservant. Spread your wing [of protection] over your maidservant, for you are a next of kin.
In those days, spread your wing over me was tantamount to saying, “marry me and become my covering.” Here is the only place where a woman clearly proposes in scripture but it’s the exception and not the rule. Some may think what Ruth did was “begging”. I beg to differ. She was simply being humble and stating her need based on advise from Naomi. The results was that a moabitess (formerly cursed as a result of coming from an incest relationship) became the great great gradma of Jesus. Does this mean I am justifying that women should propose?
Personally I am not for or against a woman proposing. The choice is left to the lady. When a matter does not clearly contradict scripture, then the choice is ours to make. I think ladies like Ruth who do it in today’s world must not be castigated for following their hearts when they have not clearly contradicted the testimony of scripture. Proposal is a private thing between the two people and not their families. Asking for a hand though is between the two families. In Ruth’s case, Ruth expressed her interest but Boaz approached the family as if he was the initiator. He did not go and say, she has expressed interest in me so I have come.
The problem surfaces when the man to whom the woman proposed turns out to be a nepios Christian and hence brags about this. In Ruth’s case, this was not so.
If a woman chooses to propose, how does she do it?
Rth 3:7-9 And when Boaz had eaten and drunk and his heart was merry, he went to lie down at the end of the heap of grain. Then [Ruth] came softly and uncovered his feet and lay down. (8) At midnight the man was startled, and he turned over, and behold, a woman lay at his feet!
I do not know process-wise how a sister should propose. For that we need Naomi 
. We are not Israelites so we cannot do exactly what Ruth did but we can take lessons from her. First the Brother should be a fellow believer. It helps to have the same value system. Second, if a sister were to ever make such a move, do it when the brother is in high spirits. For Boaz it was when he had eaten and drunk and his heart was merry. Secondly, show him that you are marriageable material. Where she lay in relation to him showed him her willingness to submit to his headship and covering. Or instead of proposing directly, just drop hints of your interest and hope he catches on.
But as I said, this is the exception, not the rule. So if any sister chooses to do this, be sure you are led by God and the Brother is mature enough not to take it the wrong way.
Here is a fun article for anyone interested about female proposals: http://www.cbsnews.com/2100-202_162-2425356.html
PS: We have possibly millions of Christian sisters whose families by tradition pay the bride price or dowry to the male and his family in places like India. Is this a negative thing? If not, then maybe this issue is merely tradition/customs dependent and not scripture dependent. And we should see it as such. Y’know partly because of the unholistic way we as a world look at the sexes sometimes, untold millions of baby girls have been killed in places India and China because the families prefer male children instead. In the case of India, it is so that the family would not have to pay out gold and other things to some man’s family later in life as dowry. Isn’t it about time, we all as a world change our mindsets?
