Well, you know your work "culture" better than anyone here, so I would say use your best judgment. Same goes with how you approach her. You should be able to use your instincts to tell you if she is interested. I know it kind of sucks, but you do have to use some level of reserve and discretion when approaching this in the face of the more "sensitive" work environment.
The easiest thing to do would probably be to feel it out a little while longer by keeping it casual. Who knows, she may even ask you out if you just keep the communication going. If after a week or two, you guys have maintained or increased the depth/frequency of your conversations, then it would not hurt to ask her out.
The group thing is a good idea, but if not, you can always suggest things during conversations by slightly leading the convo one way or another. Maybe, at work you if you end up talking to her, you can say something like "I am excited to get off of work, I have plans tonight for ..." She could always say that sounds fun... and you can reply "there is room for whom ever wants to join..."
Just use your best judgment.