Love in the Workplace

An invitation to a Friday night movie, her seemingly overt use of the word "problems," and the fact that you've been noticing her (which she might well have picked up on) do seem to suggest that she's interested. Why not ask her about the situation with the band member? If you do so casually before you respond to her date invitation, you can make the decision about whether to go out with with a clearer idea about whether this could be a date between the two of you. If you do accept the date, you'll no doubt get clear signals from her when you're out that will tip you off to her interest level.

As to whether or not to enter that territory of the Workplace Romance, only you and she can be the judges of whether the positives of experiencing what might be a unique connection can outweigh the negatives of having to see one another in the 'colleague context' each day. You should consider up front all that this will entail for you both and, if you do become involved, decide upon some 'rules,' such as "We don't share this with anyone else at work" or "It's ok for this to be in the open, but we must maintain professionalism", etc. Whatever you do, don't plan a covert rendevouz in the office; the stakes of getting caught are just too high.