It can be normal for a new layer to have a smear of blood on an egg at first. This may have attracted the hens to start picking her vent which has caused feather loss and bleeding. I agree that she needs to be removed to a cage inside the coop, so they can't peck her, but that they don't forget her. You can clean her vent area and spray it with BluKote or put some Neosporin on it for a day or two, then spray the BluKote. When you let her out, keep up the BluKote until her feathers are grown back in.
One reason they will peck each other is too little protein in the diet, too little room in the coop or run, and boredom. Make sure they are getting at least 16% and no more than 20% protein in their diet, and give them some things to climb on and explore.