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For this exact reason, I do not consider getting a girl's number, any kind of close. The only close is when you finish what you started by approaching her and getting the job done. If getting her number is so easy, I agree with you possibly leaving your phone at home to build on your time bridges and other techniques. Something I'd recommend is not trying so much to get her number, but trying to build comfort by maybe taking her to a nearby venue you have preselected. Ask her if she'd like to join you and your friends at a diner, etc. If you do happen to get her number, do not immediately leave as most others do, instead try to continue building comfort and try setting up a scenerio which she'd be likely to join you.
I think the last bit LL says here is a BIG thing. The # close shouldn't be considered the goal or the end of that initial meeting. I think it's more important to build an attraction and make sure that you've left something that will make sure she will remember you, regardless of what point the # close happens. Looking back, the most times I've run into flakes or just not gotten a call-back, it's been because I closed on the number and quickly took off right after. After, I realized that I did little for the girl to actually remember me or care that I was calling. Think of it like a first job interview: there are likely to be a number of others that have the same interview as you did, and if you didn't really do anything to stand out in their memory, it's not likely that you're going to be getting to the next stage...
Jaybot, to answer your questions from the original post, I don't think it's completely necessary to get an insta-date, if you're able to develop a good connection right there and then. Obviously, pulling the insta-date is a good thing, because it's MUCH easier to build that rapport. The best way to get that going is to justify going somewhere more private based on some kind of rapport you built up during the conversation. If you were talking about food, say that all that talk has made you hungry and you should bounce for a quick bite around the corner and come right back. I have a tendency to get pretty deep in conversations, so I usually go with something like "Man, this is getting really deep and you've actually got some interesting things to say. It's pretty loud here, so why don't we move over there so we can speak without having to yell?" Just keep it natural and make her feel like she's qualified herself for the right to be isolated.
As for giving your number, I wouldn't unless A) you're also getting her number back, or B) you're 100% sure that she's really into you and you expect a call-back. In the latter case, I'd still try to set up some sort of plans that give her a reason to call you so she doesn't get nervous and pussy out of calling you later. Regardless, I wouldn't be too positive about just giving your number out: ask yourself why she wouldn't want to give her yours?