Lots of things work on removing blood without damaging the fabric.
My favorite is Z'out; Target sells it in a spray bottle with the laundry products for about $3. You can spray it on, let it work, then rinse the spot. Repeat, if necessary.
My mil recently soaked a sweater in All to remove blood; came out perfectly! Biz also works, as does Oxyclean. The only thing I have noticed about Oxyclean is that it really needs to be fully dissolved in hot water first. When using any of these products, you want to use cold water and you may need to allow the spot to soak for awhile to give the enzymes a chance to act.