Questions: Flirting

--I want to emphasize that no one is being vilified here, and I don't want a gender war. I just want honest answers to have a better understanding--

About a week ago I spoke to a girl I had seen at a cafe a couple of times. I had chatted with her a little bit casually, and she seemed to be receptive to talking to me. So when I saw her there a week ago while I was having a small meal alone at a table, I went to her and said, "If it's not too forward of me, could I ask if you'd like to hang out sometime?" She said yes, that it was not too forward, and offered me her phone number (and full name).

We weren't able to meet until yesterday, where we had a nice conversation outside another cafe and seemed to be getting along well. Then, towards the end, she mentioned something about a boyfriend. So I waited a few minutes and asked her about what she had said, and she said she had a boyfriend, and that she assumed I just wanted to hang out as friends.

I brushed it off like it was no big deal, I smiled and didn't look visibly upset, but I was pretty disappointed. It didn't occur to me that she wouldn't think I was asking her out for a relationship.

To the question itself: Girls, if a guy by himself came up and asked you if you wanted to hang out and/or if you wouldn't mind giving him your phone number, would you think he was looking for a friend, or asking you out? Be honest about it, please. I want to know what to say.

Guys, feel free to talk about your own knowledge or experiences.

How do women feel about Serbian men, especially American women in particular.