I'm OTR right now. We got it on last night and this morning. We just lay down a maroon king size sheet, folded and a maroon towel over that. If it gets messy, we just get in the shower afterward.
FTR, we find that if he "plugs me up" with a dildo or a penetrative vibrator when going down, there is very little blood and stuff to deal with. Then we keep Eden Wipes on hand, if we're too tired to get into the shower until morning.
I'm always very aroused when I have my period. Last night was freakin amazing! (I think my heart rate hasn't returned to normal yet.
) We stayed where we fell and didn't move until morning, then into the bath and off to the bed to get at it again.
We live together, of course, so he usually knows. But, I always tell him when I'm OTR. (He usually knows anyway. I'm so peachy when I'm on the rag.) It's nice to get a warning. But, he doesn't care. He just wants sex, and so do I.