Hey, good job asking her out. The more you do it, the easier it will get to do it the next time. It’s also possible that just knowing you’re interested will plant a seed that might grow later on…maybe after one of you has moved on to another job. 
Except that from now on I’m going to be inclined to ask a girl out twice, when it’s already difficult enough to ask them out to begin with. Because even if they say yes I’m going to need to ask for reassurance that they actually mean “yes, as in yes” and not “yes as in maybe, then eventually no” which was also what happened with the previous girl I had asked out.
“Would you like to go out to dinner with me?”
“I’d love that.”
“Seriously? You’re not lying to me, are you?”
Yeah, don’t do that. You’re not likely to go out with anyone doing that.
Why do you need reassurances? Is it really that big of a thing to make plans and then have it turn out that the other person flakes out? People in general can be flakey. Especially about dating matters. Especially at your age. This kind of “Yes - oh wait, nevermind” thing has happened to me as well, and probably a lot of other people on here. It’s not a comment on you personally.
Let’s suppose that you do ask another girl out, and it does end the same way. At least you’ve learned here that the world didn’t end because of the way things went with this chick (or even the last one). So there’s nothing to lose in trying again in the future until you finally do meet the girl who is right for you and ready to date you.
I went through a long string of wasted time, rejection, and crappy treatment before I finally got together with a good man. I firmly believe that the key to dating success is sheer persistance, knowing that a lot of times it won’t go anywhere but that when you do finally meet the right person all the prior hassle will be worth it.
So, is a friendship still salvageable out of all this mess? Granted, being friends with someone you like when they do start dating somebody is one of the most unbearable experiences ever, but at the same time, females often have female friends, many of whom may be single.
While she said “let’s just stay friends” and “I would totally date you if we didn’t work together,” I’m inclined not to believe it, thinking rather that it was her gentle way of saying “never in a million years” and that from this point on she’ll make every opportunity to avoid me during social outings.
Dude, first of all, she asked you out not the other way around, you were just slow on the uptake, so don’t take any of what happened as a slight against you personally. Things happen sometimes.
Second, don’t worry about salvaging a friendship. Don’t avoid it, but don’t force it. If there is a connection between the two of you then let it happen and go slow. This is going to be as awkward for her for the next few days as it will be for you, so don’t make it worse.
Third, reread point one and remember that this isn’t about you. You work together and that probably really is the biggest reason nothing happened. Don’t lose confidence. She liked you enough to ask you out. Hang onto that for the future. Confidence is 99% of the dating game.
See if she has a sister.
Are you getting any work done?
We work in different departments. Different buildings even. I stressed that point as a last ditch effort to get her to reconsider, but no dice.
Uhh…maybe I wasn’t clear about something. She gave me her phone number after our first conversation. Her telling me to come out to the bar with her and her friends was something she said literally 10 minutes into our first conversation. I highly doubt anyone commits to a date after knowing someone for such a short length of time.
“Hey, come out to the bar with me and my friends” != “Hey I want to date you”
The first is an invitation to a social outting, the latter implies some sort of exclusive getting-to-know-each-other time.
Edit: and are you trying to imply that I missed my window? If she wanted to date me within the first half hour of our getting to know each other, I highly doubt that she’d be over me within 3 weeks, especially considering how well things were going.
And I can’t stop running that comment through my head. “I would totally date you, except…”
It’s my natural inclination to think that what she said is complete bullshit, but that’s because this girl is light years out of my league. At least she would be if we were still living with the college mentality. I suppose I have done a pretty good job at making some changes from the dweeb I was in college, so maybe I’m coming across as a completely different person. The kind of guy that a girl like this actually would date. If that’s the case it’s encouraging that I’m getting this clean slate to work with socially.
But in my mind I’m still all to aware of the kind of loser I was, and I can’t help but feel that when people look at me they can see right through to the person I used to be, the person I’m trying very hard to eliminate, and that girls like this are still going to realize that they’re just way too good for me.
So I’m conflicted as to whether her comments were genuine. I want to believe them, but am having a very hard time doing so.
I wasn’t implying anything. I said exactly what I thought. You are overthinking things. 3 years ago I was you, so I understand that what I am about to tell you will be impossible right now, but you probably need to hear it anyway.
Stop overthinking it.
Ok, no, you won’t be able to do this, but recognizing the problem is a start. 
Also, if she gave you her number 10 minutes into the conversation, you are right, she didn’t ask you out she just let you know that she was interested. A lot can happen in 3 weeks, including her realizing that maybe she shouldn’t date co-workers even if she is attracted to them.
Walk away from this holding onto the possitives, there are many. This one didn’t work out, that sucks. The next one might. The important thing to remember is a girl who you thought was out of your league gave you her phone number UNREQUESTED within 10 minutes of meeting you.
You need to start looking to reevaluate what league you are in.
So? Go with that (on the next young woman you decide to pine over). Then, instead of fifteen of you hanging out in a crowd, you’ve narrowed the crowd down to four or five, giving you a chance, during that activity, to either repeat the exercise with an event that only she might enjoy or, at the least, getting a moment to talk to her when the other three or four are distracted.
yeeesh
On to other considerations:
Stop looking for “the” woman to ask out. Ask out every woman in the group that does not repel you (and who does not work in your department). Have a nice, casual, sex-free, commitment-free experience at a movie or concert or the zoo, then ask out someone else. After you’ve asked out several, (being declined several times, of course, but getting some acceptances), then you will have several women with whom you have established social intercourse and you can start looking to narrow down your choices among them. (Plus, you’ll have gotten more experience actually asking and gotten more experience at handling the actual “dates” when you actually get more serious.)
(Alternatively, wait a few years and have your sister conspire to set you up with one of her college roommates–that worked for me.)
And this one was just the first. You now have the same job that they do and no one is aware of your past.
Relax and enjoy. 
This is good advice too. Confidence is everything here, and (despite the rejection) it seems obvious enough that you’re not a complete cabbage when it comes to this game. There’ll be plenty more chances; you can learn plenty from this one though.
Today was…good. Surprisingly good. There was no awkwardness between us. She didn’t hesitate to sit down right next to me at lunch, conversation was fine, even…dare I say flirty at times? Which just makes me a bit confused.
Anyway, I guess I’m now officially Jim Halpert.
There are worse things to be. Glad everything is going well.
My advice to you at this point - you asked, she shot you down (reason doesn’t matter). No flirting - be her friend, and that’s all. Ask someone else out. Don’t be the guy who is always available for her to boost her ego with by toying with you. She is starting to sound like someone who could play that game for years.
I second re-evaluating your league, too.
I second that advice. . . kinda.
I say flirt back, but just as practice for the next one. Don’t let her play you. You’re out of her league.
Yeah I’d say let this one go as a romance prospect. But try to be friends, you really need female friend experience.
Don’t over-analyze things. Life goes on. Even if she eventually kicks you in the nuts and cusses you out in front of a room full of people, life goes on! (Edit: actually if that happens, you’ll probably be interesting to more than a few women who were in the room! Women is funny…)
Didn’t Jim eventually get laid?