Ask once. Ask directly. Be unambiguous about the fact that you're asking for a date, not just "want to be friends?"
"Hi Jane. Listen, I like you a lot. Would you like to go out for coffee some time? If not, no hard feelings, and I promise not to bring it up again."
Yes, it's awkward, but at work ambiguity will create problems. So will gazing longingly at your crush. If you can't work up the courage to ask, then you need to get over this crush post haste.
If she declines, then do not bring it up again. Conduct yourself towards her in a professional manner. If you can manage it from an emotional standpoint, continue to be as friendly to her as you were previously, especially if you ever work together directly (women dread retribution in the workplace for turning down romantic overtures).
Treat her exactly as you would a male colleague or a female colleague whom you found unattractive. This is also what you need to do if you decide not to ask.
If she accepts, then congratulations!
Source: I'm a woman. This is how I would prefer to be treated and also what most female friends I've spoken to about workplace romance would prefer.