It is the absolute weirdest thing, but yours truly (a.k.a. the Diarrhea Queen herself - just call me "DQ") gets somewhat constipated when I have my period. It is so truly bizarre. Of course, this only lasts a day or two and then I'm back to my regular garden hose status, but it's true that your sex hormones can dramatically affect your bowels.
P.S. I LOVE the NuvaRing. I'd be a momma without it, LOL!