Should I approach a girl a second time?

Don't read too much into the handshake. Some of us do that routinely during a formal introduction. Likewise, dont' read too much into the absence of non verbal cues. I take it you didn't get any body language telling you to to away and not come back.

So far, there's no reason not to try again. Don't sound needy, and don't be too direct. Remember, you do work together. At that point, if you don't get some kind of feedback, go away.

Why don't you just get to her know her as a work colleague/friend first. You'll realise sooner or later if there's enough chemistry to go further. If it doesn't go further you'll have made a new friend and that's a good thing in itself.

Why do you have a crush on a woman you have barely talked to? Do you mean that you are in lust with her? (which is much more acceptable than being in love with, considering you've barely talked to her)

Also, while it's good know about what signals she's giving off - do you know what signals you are giving off when you speak with her?

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In relation to the handshake - it's not possible to politely shake someones hand without turning fully towards them. Anything else comes across as supremely disinterested, and is considered rude. Many women won't do anything to purposely hurt someone who hasn't given them any cause to hurt.

In relation to the other body language - it wasn't particularly interested, but it wasn't negative either...so you can try again (there was nothing in there that you described with is 'dismissive')

If you know (or can find out) what kind of coffee she likes - why don't you take her one (with a cup for yourself of course).
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One good way to overcome anxiety is to practice. In this case, as it's approach anxiety you have....you can make it safe by practicing body language as you speak, while imagining approaching someone.

On the the things about our mind is that it can't truly distinguish between imagination and reality. If you imagine approaching her, looking in her eyes and saying the words...you should find that your heart rate starts to increase, your voice may crack, you may crane your neck forward, you may stutter (or just not say the words at all like you would like to). Practicing helps reprogram your mind.

What you practice you gain confidence in doing...if you think about it - this is the same for any skill you possess. The mind skills are a bit more difficult because they are so much more complex, but when it all comes down to it, they follow the same basic rule...the more you practice, the better your confidence will become in what you practised.

You need MUCH more experience with women in general. Consider joining a co-ed sports team or some kind of group where there are men and women doing something together. Find out what your community education or recreational depts. are offering. Even go to a lecture or theater series. De-sensitize this great fear or hesitation to approach a woman.

And hurry up - winter is coming.

short answer, yes approach her again.

If she's never talked to you before, or noticed you, you shouldn't expect her to just immediatley show interest.

Think about it. You had the advantage of scoping her out for awhile to form an opinion, let her do the same.

I don't think I've ever flipped my hair at a man in my life. I think all that stuff is silly.

Just talk to her a few more times and let the 2 of you get to know each other.

vikorr, a crush is just a crush. It's that initial "pow, I think you're attractive" thing.

it's not being in love with someone.

Well, for interests sake - given the OP's personality, I disagree quite a bit - crush is another word for infatuated. For a shy guy, that's a bit of a problem when he's only once talked with the girl. If he realised he's just in lust, then it can help change his mindset.

'Pow, I think you're attractive' is a very different experience for a shy guy - that's the short term/initial version...but he's had a crush for a while it seems.

Well, I approached the girl again today . I still had nerves, but it was less intense this time. I think I got a warmer response, but I might be wrong. She made more eye contact with me this time. I noticed that in response to that I involuntarily was avoiding eye contact. My eyes were going all over the place. I'm guessing it's because she's really cute and looking directly at her for more than a brief moment made me uncomfortable. Fortunately, I noticed it and put my eyes towards her.

The conversation went a lot smoother than the first time. She wasn't turning to her laptop every so often so that made me more comfortable. Maybe she has a boyfriend or maybe she's not my type. I don't know, but at least I can say I'm building a rapport with an attractive girl. If it doesn't lead to a date, this would be a stepping stone to approaching other girls in the future.

Once again, thanks a lot for the replies. I know you guys could be doing something better with your time than replying to posts from socially inexperienced people like myself.

Oh and Punkey, I liked the GOT reference in your post. I'm eagerly awaiting season 2 on Blu Ray.

You think too much. Just be yourself. Relax and appreciate the small things.
Fooey on all the experts! What qualifies ANYONE as an expert when it comes to matters of the heart? One girl flips her hair, the other envelopes herself in her laptop. They could very well both be attracted to you.
You have a great advantage here in that you work together.
Try asking about her department, projects she is working on...etc. Let the conversation be your focus, not how cute she is. She will likely appreciate that you are taking a genuine interest in her. Be patient. There are plenty of cute girls out there, but if she's on her laptop plotting with Al Qaeda, you're not going to see "cute" any more. Find out whether or not she is someone you would want to spend time with.
She's probably on your company email roster. Maybe initiating an online conversation as you move forward will be more comfortable for you both.

No after all this , you must not approach her again, If she say sorry then you can think , but be careful next time.

I say this is bad to start with. For one, you work with her? If I understood correctly if she is a co-worker it can be disastrous to date a co-worker. This is bad form. It could work out, you date her for a while and then what? What if she decides you are not her type? Horrid work environment from that point on. So only date her if you don't like your job and plan to leave it if things turn bad.