[This was originally a reply to something papserweight said, then Jordan posted as I was finishing up, so I’ve rejigged it a little to adapt to that, which may be a flawed choice…]
I wouldn’t put a blanket ban on asking out people at their workplace, but I would set a high bar to clear before acting, and urge a particularly careful and considerate approach to the situation – rather than asking the person out, you’re asking whether you’re reading the situation correctly (something like, “Hey, this is awkward to ask, but I get the vibe you’re into me and I want to check if I’m misreading you?”). You need to be aware that they may try to reject you in a non-confrontational way (given that some people, particularly men, react badly to any sort of rejection) and you could misinterpret that, so it’s best to take anything short of enthusiasm as a “No”, and be ready to apologise in an appropriate way (along the lines of, “Sorry about bothering you at work, it’s just the uncertainty was feeling a bit awkward ”). And, of course, be ready to advance things if there is genuine interest, preferably by putting the ball in their court (e.g. giving them your number and saying to hit you up if they want to get to know you).
In this case the hearts on the cup is not a sure sign, as I can see potential for her to come to the idea from a different place (it’s quite possible to derp one’s way into something easily misinterpreted), but it does give you a fair basis to ask that clarifying question: whether the hearts mean she’s interested in you, or they were just a drawing.
The exact phrasing depends on what fits with you, but you need to keep it brief (minimising the demand of her time + minimising the risk of stuffing it up ) and you’ll preferably include a nod to it being a potentially uncomfortable interaction, avoid pressure, and make it easy for her to reject you if she wants to.
You want to be in and out of the discomfort-zone as quickly and painlessly as possible.
P.S. Dynamics are a little different for women asking men, since men get hit on infinitely less (along with some safety-related aspects), and in that case I’d be inclined to tell girls to just go for it. I won’t speak to woman-woman or man-man situations, as those are very different kettles of fish with a whole different set of factors (accuracy of gaydar, closetedness, potential for homophobic reaction…).
P.P.S. I’m typing this while I’m recovering from the flu, so hopefully it isn’t too ill-considered .