Come on, OP.
I'm probably in the wrong here, but if you insist on riding this situation out, at least be looking on the side for potential hook-up material. By all means, don't cheat on your girlfriend of three weeks who is sleeping in the same bed as her ex, but just make it so you know that you could, at any moment, be in bed with another woman if you so wanted.
So when the most likely scenario plays out, and you find out that her ex isn't shadow boxing in the sack unsolicited, you won't feel quite as bad. And you'll have a rebound ready to rock.
Or do the sensible thing in this situation and call an indefinite break to this relationship until she sorts her situation out once and for all. If she's serious about you, she'll figure things out. If not, not.
Honestly, if you were just casually sleeping with her, there'd be no reason for concern (er, less reason), but the fact that you call her your girlfriend is telling me that you are already emotionally invested enough to get burned by this whole situation... Tread carefully, OP. Try to distance yourself a bit from this powder keg until you are certain the coast is clear. A break is the right play imo since it doesn't have the seeming finality of a break-up, and thus you'll more likely have the stomach to pull the trigger on the former over the latter. Good luck!