Covering My Head Amongst A Cover-free Congregation: Do I Dare?

In some schools of Christian thought, a woman is expected to wear some sort of headcovering in worship if at no other time, but the man is expected not to.  These people look to the following passage in the Bible:

"Now I want you to realize that the head of every man is Christ, and the head of the woman is man, and the head of Christ is God.  Every man who prays or prophesies with his head covered dishonors his head. And every woman who prays or prophesies with her head uncovered dishonors her head--it is just as though her head were shaved. If a woman does not cover her head, she should have her hair cut off; and if it is a disgrace for a woman to have her hair cut or shaved off, she should cover her head.  A man ought not to cover his head, since he is the image and glory of God; but the woman is the glory of man. For man did not come from woman, but woman from man; neither was man created for woman, but woman for man. For this reason, and because of the angels, the woman ought to have a sign of authority on her head." 1 Corinthians 11:3-10 (NIV)

In the churches I have gone too, there'd maybe be one or two women who wore hats, but otherwise, it was all bare heads all around.  Growing up, I accepted this without question. This is not something that came up, ever. But I started wondering about the concept when I had read about this verse sometime in college. (I was looking up stuff regarding the concept of biblical modesty.) I want so badly to try and make sense of the concept and maybe see if wearing a scarf or something will help me make sense of it.

There's a problem with that, though. At both the church I am a member of in St. Louis (a Disciples of Christ one) and the Baptist one that I've been attending in Pittsburg a couple of weeks or so after I had left St. Louis under circumstances beyond my control, there is not a single headcovering of any kind to be seen. At the Baptist church I attend, I am one of the younger people there, and I'm not even an official member, I worry that for me to wear even a hat or scarf, even if I don't say anything, would call undue attention to myself and create too much of a stir. (Some schools of Christian thought teach that a woman's long hair is her covering. I know I can at least get away with that even though a lot of women in the congregation don't even do that.)

For the time being, I keep a sheer black scarf (which is cut like your average bandanna) in my purse. Maybe one day, I will be brave enough to wear that (or maybe a hat or other covering) in church, such as when I'm older or if I marry a preacher. That way, if any woman who comes along becomes convicted about the headcovering or starts to wonder about it, she won't have to feel as self-conscious about it if she sees someone else doing it.