I find it charming when I am approached by a stranger...I admire the confidence, the vulnerability, the courage that it takes...of course, I am not in the market, but I thank the person, and sometimes we will even share a cup of coffee and just talk for a bit with no expectation...nothing ventured, nothing gained.

You answed it yourself, start a conversation about whatever, you will know soon enough if she is receptive. No creo en Dios!

I think the whole approaching strangers in public for dating purposes thing is such a crapshoot! You have literally nothing to go in except appearances! What are they odds that a random person you approach is going to meet your basic dealbreakers, let alone have anything in common with you?