IMHO, you should just bite the bullet and ask her for a drink after work or something. Then at least you KNOW where you stand.
No fancy dinners at restaurants, just a drink in a well-chosen bar. I would suggest a bar that has some kind of feature (e.g. a pool table, a quiz night etc.) as it will give you something else to focus on and help prevent any awkward silences developing.
I'll let you into a secret... girls love self-confidence. So even the way you ask her will suggest this. For example, instead of saying "Would you like to go for a drink sometime?" you could say, "We get on great, we should go out for a drink sometime". The latter takes away any sense of self-doubt (and it also makes it harder for her to say "No"

). She'll either say, "
Yeah, for sure" (happy days) or she may say "
We'll see" (basically a polite "no")
A word of warning, if she invites (or suggests inviting) other people (even if it is her "bestie") then consider that her letting you down gently.
Even if it doesn't work out, just be grown up about it, and there shouldn't be any awkwardness about it (That typically happens when one person can't handle a rejection).