There’s no Biblical requirement for a woman to submit to a man before they’re married, but if she’s rebellious before marriage, it’ll only get worse after marriage.
In other words, she’s not required to submit, but he’s not required to marry her, either.
Precisely what I recommend in Practical advice to single Christian men establishing leadership and the right frame when starting a relationship.
If we look at Jesus’ life we can see He offers to become the “head” of the disciples / Church by asking them to “Come, follow Me” and then He leads and teaches them. They voluntarily act according to what He is teaching them about God and how to live life in accordance with how He is going to change the world. John 6 also shows that many disciples who disagreed with Him left Him in great numbers at one time as well.
This is an excellent model to show the types of “bid and response” we would like to see in men and women while dating and then engaged and subsequently married.
I am often fond of making the point that you are the same person that you were before you got married as the day after you got married. So the the potential spouse, whether a husband or wife, is not going to magically change upon saying vows. If they’re an untrustworthy or unfaithful person before they say their vows that’s not something that changes in the snap of a finger. The same is true of attitudes and actions held by a man or woman because of one day or one commitment (except, perhaps, accepting Christ who can break those chains immediately, though, usually we see gradual sanctification). Who they were before that day for weeks, months, and years is going to be the same person after marriage. The trajectory of their growth pattern or already having the long term habits of obey God and being faithful with the small things and big things is the most important.
The key then, for both sides, is to make good “bids and responses” in terms of proper headship-submission and love-respect lines. The man should show leadership and see how she follows. The wife should be trying to follow and see if he exhibits good headship. The husband should love his wife and see if his wife respects him. The wife should respect her husband and see if it helps him love her more. Building up these good cycles and habits start to hedge against bad behavior from cropping up and going into more destructive behavior cycles.
Obviously, one should be doing these things irregardless of how someone is treating them as God shows us in that while we were yet sinners Christ died for us (Romans 5). However, we are not required to marry and thus we should be choosy of only someone who is wants to and is willing to do these things without having to have pressure put on them to do it. If they aren’t willing to do things when there’s no requirement, it’s unlikely that they’ll do them when things get tougher like when tough times can come during marriage.
In these we must always be reminded that God’s mission and our sanctification are the end goal.