First of all, DON'T ASK if she's on her period, and especially don't call it something stupid like Aunt Flo or the Monthly Gift. Asking implies that it's only okay for a girl to act like a bitch on her period, and that is 50 shades of false. If she mentions casually she's on her period, act like you didn't even notice the brownie crumbs on her shirt or the passive-aggressive subtweets aimed at her ex.
Don't say anything could be interpreted in any other way than how you intend, which should be kind, nice and generous, but not too much of either. For example, just today my boyfriend asked if I had been to the gym, which obviously means he thinks I'm fat, which means he can get the heck out of my house. (I stand by my previous declaration that I would never date myself.)
Now is not the time to break plans with or offend this girl. Grudges established during period week are the hardest to appease. Hold off on any bad news or beauty suggestion until the train has departed Menstruation Station. Do not ask her to go anywhere that requires strenuous activities, rationale, and definitely no bikinis (are you TRYING to make her feel ugly??).
Lastly, accept that Period Week is the only time girls can get away with everything, because everyone knows the universe gangs up on a girl during her period. Absolutely anything can be blamed on it. Zit? Period. Bad grade? Period. Speeding ticket? Period. Global warming? Period.
Sometimes you just have to menstru-wait it out.