I think I understand your gf's feelings...
When I cry, I don't like people crowding around me. I prefer to be
left alone, to sleep it over.
But I think the best thing you can do at that moment, is to just
sit next to her and keep quiet, and offer tissues. When she's
ready, she'll probably spill her thoughts. That is, if she is
willing to share. Not that she doesn't trust you or anything, at
the least in my case, it's some sort of insecurity thing..
I think that firstly, it depends on the problem, whether it is
related to you or not. If it isn't, then you can probably lend a
shoulder for her to cry on. Don't ask about the problem; wait for
her to open up. Give her tissues and soothing rubs on the back
etc.
Edited:
Or maybe she's just insecure.