It sounds like you're leaning a little too hard on your shyness, when you're clearly enterprising enough to consider some pretty adventurous maneuvers in the workplace. 😉
I'd recommend you first list out everyone you're attracted to at work, and perhaps class them by how sad your personal and professional lfe would be if each of them never spoke to you again. Then, for the "least valuable" possibility, recruit her as your wing/confidante, asking for help in meeting women, showing off your best side, etc… Don't involve her in your plot to pursue women at work, just in general.
With luck, she will have some pity on you, and perhaps introduce you to a few guys who have skills, or take you to a party or two filled with her available friends.
The main goal is to pursue at least one total stranger first, for every woman at work you are attracted to… This is mostly to gain relevant experience and confidence in simply having bad dates – after the first few, it definitely sucks less, and you start to learn which things you can work on to improve the outcome overall… It also helps to keep at least some of your social failures isolated from the workplace… While there are varying levels of stigma attached to pursuing a coworker, there's pretty universal derision for those guys who pursue multiple workmates, as it seems quite LAZY and not a sign of a confident capable and desirable partner.
I could go into further detail, but each case usually has its own twists and turns that would go against more general advice… I'd be happy to discuss your individual case one on one (no charge!), once I know more of the details, I can help devise a specific "training program" to get you to the "top of your list", and at least give you a fair shot with her.