What is wrong with being a third wheel?

Okay, hear me out. This isn't going to be one of those mushy "OMG I met a girl!" type of posts, but some background is needed to tell the story.

I was finished up shooting some footage for TV Journalism when I came back to the campus to wait for my next appointment which was two hours away. In my wanderings about campus, I met somebody I knew and we got chatting. She had to meet some friends in the tavern so I decided to tag along.

So she didn't find the friends she was talking about, but found a friend, drawing. She wandered off, but I decided to stay and ask him about what he was drawing. We got to shooting the breeze, killing time when a friend of his came up and sat by us.

Then, another friend of the friend sat by us. The first two left, leaving me and an extremely cute girl to talk. As I said, this isn't going to be one of those "OMG I'm in lurv!" kind of posts.

She had strawberry blonde hair, was an english/journalism major, was into Harry Potter and Vodka Cruisers. We talked Shakespeare and feminist authors in Australian literature. As far as first conversations went, I thought it went pretty damn well, and I was so close to asking her out on the spot, but something stopped me.

Now, I'm not one of those guys who can ask a girl out cold. I've got to work myself into a state of zen and then pump myself up for days to get the nerve to ask a girl out (Yes ladies, I'm one of those cute guys who you hate because they won't make the first move).

But what ultimately made the decision not to ask her out for me was the fact that I was a random. I wasn't looking the best either, but I was just some guy she was meeting for the first time, and her friends were all about.

I guess my question is, can you ask a girl out if you're a random to her? Do you need at least a two conversation minimum to take the relationship to the next level? Is it perfectly acceptable in today's society, within an hour of meeting a girl, to say "Hey, I think you're cute and I'd love to take you out some time"?

I'm of the school that you do, but then again, I'm a pretty shy individual, despite my bravado. But what do you think? Is it polite to ask a girl out within an hour of meeting them?

P.S- I'm hoping to 'bump' into her again

P.P.S- If by any billion to one long shot you're the girl I'm talking about, come and find me. I think you're cute and would love to take you out some time.