Whether Rufus injured himself or he injured somebody else, the result might be the same: blood all around. Fresh blood is relatively easy to clean off a dog's fur -- just give Rufus a bath and it will wash away as you rinse. Dry blood is a bit trickier to get rid of, but certainly not impossible.
Check Doggie for cuts and to see where the blood is coming from. Is it possible that the blood is not hers? This will change the way you deal with the blood -- if Doggie is hurt, you don't want to clean too close to the injury and risk pain or restarting the bleeding.
Wet a thin towel or cloth with warm water. Rub the area with the blood stain and see how much comes out. Remember to rub gently if you're working around a cut or an injured area.
Wet the cloth in hydrogen peroxide if water alone doesn't work. Peroxide is commonly used to clean blood stains from linens and clothing because of how effective it is -- plus it has the added benefit of being a germicidal agent. If Doggie has a cut near where the blood is, cleaning it with peroxide could help it heal.
Use a jumbo size cotton swab to clean the blood if it's sitting near the wound. Simply wet the cotton swab with warm water or peroxide and rub the dry blood. This is safer than using a towel if you're working around a wound, since you can control more easily where you're touching.