Rust remover is great on blood
But I would not be using it on that type of fabric without pretesting!! Be warned. I once made a small 5 pence piece sized pink stain using it on cotton fabric. Luckily it was no where to be seen as it was the pre-test. I tried to reverse it with baking soda but didn't do bugger all.
Enzall would be my choice for that (or your enzyme of choice but everyone knows enzall is the daddy). Mix it with hot 60 degree water to release the enzyme action and dissolve the product, then cool it down before applying it to the stain, then rinse.
Again, make sure you dry thoroughly before packing up.