Vaginal intercourse during menstruation is maybe not the tidiest of experiences. In fact, it can be downright icky for a fastidiously clean person. If it grosses you out but you still want to try, tools you can try to make it less of a mess include a diaphragm, a cervical cap, or a flexible catchment like the Softcup, which surrounds your cervix up inside of you, out of the way of the action.
Or if you don’t want to mess with anything invasive to curb your menstrual flow, just do what you’ve probably already been doing: lay dark towels over your sheets and wash them by themselves afterward. Or have sex in the shower. Win-Win.