But seriously... why not just leave to "get a coffee", and offer to bring her one... next time, ask her if she wants to come with (assuming it's a set break time or there's a lull) - use something like, "Wow, kinda stuffy in here, wanna go grab a quick coffee and some fresh air?" If she doesn't want to go, then go anyway, and bring her one back (now that you know what she likes). When you come back, act all refreshed and relaxed, like getting out of the room really did you good. Won't be long before she'll accept the invitation. From there, it should be easier to get her to go for a coffee AFTER work/class... then dinner on the weekend... etc.