I haven't done this with a chicken, but it worked wonders with a little of kittens that were mauled by a stray tom. (Tom (and Mama) got neutered/spayed that weekend - and the babies, at least the ones that we got to - all survived.)
Our vet reminded us that blood is water-soluble, so try warm water, first, especially if you suspect injuries under the blood. If she'll let you hold her, try saturating a clean gauze pad or a piece of lint-free cloth (think muslin or white tee-shirt) in warm water. Rest it gently on the bloody spot and let the warm water do its' thing. Don't use cotton balls - the strings can catch.
Keep changing your water to keep it clean and warm. You can rinse the area every so often by squeezing warm water out of a clean cloth (pouring the water over gives you less control and you could end up getting water in her lungs.) Whatever you do, don't try to work any clumps of dried blood out with your fingers. You may well end up with a fresh bout of bleeding - and that's hard to stop!