With shy girls, things must be taken slower, and no immediate intimacies...how do I deal with her?

I approached her today and said ';that was great, you sang really well';. I could talk to her next thursday too as we have Rock Workshop at the end of every thursday...when should i offer to buy her lunch uptown one breaktime? next couple of thursdays? i should take things slowly. both of us are basically introverts lol we are polite and friendly. lot of advice on here involves chatting up girls with all the touching and whatnot obvious signals. I'm just interested in her. I don't generally go out my way to get friends let alone a girlfriend.With shy girls, things must be taken slower, and no immediate intimacies...how do I deal with her?
i don't know exactly your situation but being a shy girl myself being approached and singled out can make me nervous/annoyed. it might take a little longer but you should try getting close to her friends maybe not even her close girl friends but just guys that hang out with them sometimes that way it'll feel more natural to her and not so much like an attack. The signal thing is super hard and they'll probably mean for you to go away/'brushing you off' at first because she feels uncomfortable in social situations but stubborness aside keep trying for a while to see if you can break through her barriers if not there's plenty of other girls out there yadayada and all that junk... good luck