Sotos wrote:I think it was a mistake to ask her out from the first time you talked to her. Instead of keep looking for her for days you should have found an excuse to talk to her earlier for something unimportant like the weather or something better depending on the occasion. Then since you see her every day you could say hello to her every day and maybe exchange a word or two. Then after a while you could have asked in an indirect way to find out if she is available. Then instead of lunch offering her a coffee at a cafe would probably be a better idea. Conclusion: Take it easy and don't rush!
I agree with everything what Sotos said. You got to be careful, that an "eye contact" is mutual, so that she knows that you exist, but she does does not feel like she is being stalked by "Jack the Ripper". It would have been useful to know if she is in a relationship or not before inviting her to lunch. Since she said no, for now, it is best to give her "space". She may like you still, but she needs time to think about it. She may also be shy. You can have small talk with her when it's possible, but do not stare at her. If you catch her looking at you, just smile back and either wave or just say hello. In time, if she is interested, since she knows that you're interested in her, she will let you know. If you continue being in each others "SPACE", and talking to each other has taken off into a level higher, and you know more about her, then invite her for a coffee.
Be cool and do not rush. Most relationships starts with the Girl saying "NO" first, so don't be discouraged.