Would this be cool or will she think I'm a creep?

[Dagless]

BTW..I'm happy for you that you're thinking about getting out there and dating.

 

I've only just noticed this post! Thank you, that means a lot.

[lila...]

That's not a good tactic. It's like you're giving her permission to call you. It should feel like the other way around for her. Even a simple, "Let's get a drink together... do you have time this week?" should suffice.

 

I agree with this. You should exchange a few words and glances before you give her your number. She almost certainly won't call you, especially if she's the shy type. When a guy I barely know gives me his number, I more than likely won't call. I wouldn't like all the pressure to be on me. I'd rather he take the initiative to talk to me and get to know me a little before I feel comfortable enough to call him or accept an invite.

[scotty77]

I think you need to break the ice and make an excuse to talk to her and see how the first conversation goes.She may be friendly or ice cold[which will kill any advance].If the conversation goes well,you can then launch into phase two,attempt another conversation.I have a feeling you are going to chicken out from asking her out directly,so if the first two conversations go well,maybe you could ask for her email and send her an email asking for an invite of some kind. A face to face encounter is always best though and I think your odds are better if you do it that way.Only give her your number with the note[as you originally planned] if you have conversed a couple of times [and it goes well] if you feel that you absolutely won't do it otherwise.You said she works in a different department and you don't see her that much so if she isn't interested ,you aren't going to have to see her anyway.