As a hand appliquer, I am always jabbing myself and getting blood on my blocks.
I was told years ago that your own saliva will take out blood. It works, on new blood anyway, not sure on dried.
I usually immediately wet the spot with my saliva, and wash in cold water. Presto, the spot is gone.
Don't know if it will work for you, try wetting the spot with cold water, then your saliva, wait a couple of seconds and then wash again, repeat if you need to.
Hope it works, let us know for future reference.