All singles who profess Christ and aspire to marriage — even as a possibility — have this responsibility (even outside this area of life, we should all be trying to grow in Christ). If you're already sure of that basic answer, are you a growing and mature Christian?
Are you generally humble and teachable, and do you respect authority?
Ladies, this doesn't mean that you have to cut your would-be suitor off mid-sentence, take off running and shout your father's (or whomever's) name and phone number over your shoulder as you go.
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.
The command in Genesis to be fruitful and multiply is a general command. As it is the man's God-given role to initiate, so it is the woman's God-given role to respond.
When Paul extols singleness in 1 Corinthians 7 (which is an often-misused passage in this area of life), it is singleness for the purpose of enhanced If you are floating around staying single because you enjoy social flexibility or having time to yourself or hanging out with the guys or because you have worldly ideas about the perfect woman or how to approach marriage, consider: Are you approaching manhood and marriage biblically? Her response may be positive or negative, it may occur through her father, her family or words directly to her potential suitor.
As I mentioned, he should not do this until he is "ready" to marry.