As a practical matter, are you responsible and holy in the way you possess your own spirit, mind and body?As you move into the stage of life in which you begin to seriously consider marriage generally or a particular relationship, your first step should be to soberly reflect, before God, on your own spiritual walk and maturity in Christ.
First, the man should initiate asking the woman out.
Whether this means approaching the woman herself or her father or someone filling that role instead of her father, it should be the guy that starts things off.
As I've written on this site before, "practice" and "recreation" are not good reasons to date.
Dating is for the purpose of finding a marriage partner.
See what an unsatisfying bumper-sticker treatment that was? Among the different roles assigned to men and women in the Bible, men are assigned the role of leadership. This is not a signal of male superiority or of the greater importance of men.
It is simply God's design and assignment of equally valuable roles among spiritually equal beings. Briefly, biblical support for this position is found, among other passages, in the creation order in Genesis 2, in 1 Corinthians 11: 7-9, and Ephesians 5.
Ultimately, this means learning to trust God's goodness and sovereignty.
Clearly, this is not the popular secular view of the "liberated" woman's role.
In my view, if you can't happily picture yourself married within a year, you're not in a position to date.