The blood in Blood, Sweatshop & Tears comes from the inevitable (but fortunately infrequent) jabs from pins. So far, I’ve been lucky not to bleed on anything, but if it happens, I know what to do.
Spit on it. (Saliva contains enzymes that break down blood.) Get the spot good and wet. Then rub the fabric together, or scrub with a toothbrush.
I have heard that this only works on your own blood, but that’s not true. I once sparred with someone in a karate class who had scraped his knuckles, and he dabbed me with every punch. Blech! Little marks all over my shirt and sweats, but they all came out. (Needless to say, I gobbed on the clothing from a distance as I was not keen to share fluids.)