When opportunities presented themselves, I'd smile and say things in passing to her when I'd see her in the hall or when I'd walk past her when she was seated and not talking to the people around her. This led to a sort of friendly familiarity. That led to us talking as we walked to our cars, which led to me asking her if she wanted to grab some coffee, which led to her saying yes.
Again, using the example of the woman I asked out, it's a group of people (all in their 60s except her) who are all seated together and talking to one another (and all are married except her). There was no opportunity to inject myself in a natural way.
And another example I can think of is a woman who always comes with another couple, usually late, and they sit in the middle (again, of a big church). Finding an opportunity to speak to her was tougher than finding an opportunity to speak to the previous woman. It eventually happened one morning when she was running late and we were both in the parking lot at the same time. I made small talk to her, but didn't find her friendly or personable at all and immediately lost all interest. One thing both women have in common, I discovered, is that they are both fairly recent widows. That may be why the second woman was unfriendly. I can only imagine the difficulties widowhood brings when it comes to being ready to date. The first lady managed to be very nice about it, while the second woman gave me a small case of frostbite. And, again, I am not criticizing her for it.
It is mostly couples and families sitting together at my church, too. And often when a woman is sitting alone and I start to wonder if she is single, I catch the glint off a wedding ring or her husband comes to join her later. This has happened over and over. Single women should have to wear headbands or clothes that are a certain color for easy identification.
I can't emphasize enough that I am not shy. If there is a woman I am attracted to and I have an opportunity to meet her in a non-weird way, I'll walk up and meet her. That is rarely the case in the context of my church's services. I've also tried home studies and virtually everyone is married. I also signed up for a couple of classes (Financial Peace and a Creation Science course) and everyone was married. So, I stand by what I said in my opening post.