How to respond to female coworker playing hard to get?

I have confirmation that a female coworker likes me and is interested in me, but she is playing hard to get. Before anyone tells me not to date a co worker, let me explain that we work for two different companies(I work for IT outsourcing company, she the company that contracted my company), we work in two different departments and can go several days or more without seeing each other. I normally do not like to chase to date, but there is something about her that makes me want to fight for her, she has the "it" factor to me.

I sent her an email and I will not say verbatim what the email said, but it in I played my own mind game. She either was going to say yes to going out, no, or ignore it. She ignored it and by doing so validated her playing hard to get. I basically flipped the script to gauge her interest. I sent the email so I can have a written record of me pushing her for an answer or I will pursue her and that email was her way to say "NO" not interested so she cannot report me for harassment. By her ignoring the email I validated that she is playing hard to get and has not said NO, despite my several references to me telling he she can say no and I will not pursue and will discontinue the interest.

So my question is how do I act now that I know she is interested and playing hard to get? My plan is to just act like business as normal, and say hi in passing or cafeteria and kind of ignore her a bit, but still show my interest here and there.Let me remind everyone out there that SHE was the one who initiated the contact and the flirting and we have been flirting for two months before I asked her out.And I have so much evidence that she likes me that if this was a jury trial this would be a slam dunk conviction. And despite her ignoring my email she still sends body language signs that she is interested.