I had ruined yet another pair of panties during my period, and I noticed my bottle of peroxide on my counter. Remembering that I had read that it worked for blood stains, I poured straight peroxide on the spot, watched it fizz up and promptly put the underwear in the wash. It was gone! It doesn't completely remove older stains, but it definitely fades them.
After you cleanse the cut on your finger with hydrogen peroxide and find the blood got on your favorite shirt/blouse, use that same hydrogen peroxide to remove the blood from that article of clothing. Just soak the blood stain with undiluted hydrogen peroxide for a for a good five to ten minutes. You will be able to see the blood vanishing before your eyes. Rinse with cold water and wash the article of clothing as usual.