Salt will clean blood out of any fabric, even the whitest clothes or bedsheets.
Just put a little heap of salt over the bloodied fabric. If the blood is dry, wet it with a few drops of cold water then put the pile of salt. Leave it for an hour or so, wipe the bloody salt off, then wash with soap.
Edited to add that the water should be cold - see comments below about hot water setting the stain
Edit 2 for people who menstruate:
An early or particularly heavy visitor can lead to embarrassing situations sometimes, especially if (like me) you have woken up on a Japanese flag while sleeping over at someone else's house or at camp. Regular old table salt is something you can find basically anywhere you go, at any time of day or night, without arousing too many questions. You can pour a heap of salt on your stains (and put a few drops of cold water if the stain is already a bit dry), and it should be soaked up before too long. It will take the blood out of mattresses, sheets, and pajamas/underwear.
An early or particularly heavy visitor can lead to embarrassing situations sometimes, especially if (like me) you have woken up on a Japanese flag while sleeping over at someone else's house or at camp. Regular old table salt is something you can find basically anywhere you go, at any time of day or night, without arousing too many questions. You can pour a heap of salt on your stains (and put a few drops of cold water if the stain is already a bit dry), and it should be soaked up before too long. It will take the blood out of mattresses, sheets, and pajamas/underwear.