I am definitely no expert on courtship myself, but sinse Johnson asked for input from the ladies, I decided to post.
I would agree with some of the earlier comments that during those initial interactions with a person of interest you know, you
know when someone likes you. Like Johnson said there are those (non-flirtatious) vibes that are exchanged that give clues that someone is interested. Personally, I prefer to get to know someone in a group setting because I have had bad/awkward experiences with hanging out 1-on-1 with a guy who seemed "nice" and approached me in church with the intent of getting to know me better. I agree with Johnson that for better guarding of each person's heart and to avoid putting pressure on any one person, group settings are best, plus they are more fun.
Now this is just me, but personally if a guy approaches me wanting to go on a date alone after only knowing him for a couple weeks, then it immediately raises red flags... My first thought is, ok, why is he trying to get me alone so soon? Can't we continue to know each other around other people first?
My thought is that the 1-on-1 stuff needs to happen in the context of courtship (but not being 1-on-1 ALL the time) where there are set boundaries stated and accountability identified and many caring and watchful eyes around. In courtship it is acceptable to develop the "us" and the "couple" identity because there are stated intentions and a purpose with an end in sight.
As far as guys being the initiators, call me old-fashioned, but I completely agree. Men were created to be initiators and pursuers and women are created to be receptors and responders. It just...works better this way.
As Johnson said, this does not mean that guys abuse control or that girls become doormats, but the Lord has designed men and women this way to establish His divine order. He wants women to rest and trust in Him to tell the men what to do, when to do it, and how to do it. I'm not saying that trusting the Lord is easy, because at times it is not, however, a man that is in tune to the Holy Spirit's leading will know what needs to be done and will do it at the appropriate time.
But that's just me...

any other thoughts?