Girl Friends

Sometimes I meet girls through other friends, work, or volunteering, and I want to get to know them better, or hang out with them again. I find it awkward though, and I don't think I'm alone in this. Sometimes it's just as scary to ask a girl for her email or phone number as it is a guy, and I mean this in a totally straight way. When you really hit it off with a girl, in a platonic, 'this girl is cool and would be fun to party with' kind of way, why not end the night by asking her for an email so you can hang out again? At least Facebook is so common that it's relatively un-creepy to add someone the next day, but it can still prove to be a difficult situation. A common in-my-head discussion as I leave one of these situations sounds like this; 'Did I come on too strong? Did she think I was cool? Did she enjoy our convo about sketchy guys as much as I did? Would it be weird if we hung out just the two of us?'.
Why do girls freak out about this so much? First of all, I don't want to be mistaken for having romantic interests. I have nothing against lesbians, but I'm not one. Secondly, I don't want to seem pathetic or desperate. It's almost like I want all other women to believe I have an amazing social life and do not need their friendship. Yikes.
I have (mostly) gotten over my self-consciousness, and if I really enjoy my time with someone I make an effort to stay in contact. Most women I know are flattered when someone new wants to hang with them or include them in their circle. For me, meeting new friends means exposure to new restaurants, bars, shopping and activities. And I guess if a women can't pick up on the fact that I'm straight from my many random dating stories, then there's a bigger problem at hand.