For the women who genuinely do not understand how a bedroom (or kitchen, or lounge..) could possibly NOT look like a "slaughterhouse" after having sex while on the period, here's a how to:
a) If you wear a tampon/mooncup and remove it just before sex, and wipe your vagina or have a shower beforehand, the vagina is cleaner and there is less blood to spill.
b) No matter how heavy your periods are, surely in 1 hour that sex may last you cannot lose litres of blood? If you did, you'd die after some hours hours on your period. And yes, we women who choose to have sex on our period tend to avoid the heaviest day. Or not, shock horror, if the prospect of sex is too tempting :)
c) The penis being in the vagina does tend to stop most "spilling", in the same way that semen often does not spill out till the penis comes out, so you can actually have a towel ready when he comes out and voila! Most of the blood goes there.
d) Unless one of your sexual fetishes is rub yourself all over your lover with your vagina like a slug, the man does not end up "covered in blood".
e) Semen actually dilutes the blood, so the resulting small stain actually looks pinkish and not that gross for the majority of the population.
f) When you have sex on your period you are indeed a bit more careful about positions/where a small spill may happen, the same way you'd be careful if you had an injury/a cast/a bandaged wound, and you modify sex accordingly, so yes, swinging off the chandeliers may be off for a couple of days. But I swear to you, it really is not that gross or that complicated. Pinky swear.
My - apparently very popular - comment had nothing to do with telling the OP what to do, I couldn't give a flying fig what other women choose to do with their sexual partners. It was a way to show surprise that having the period seemingly automatically ruled out sex.