I also have a hen with a bare bottom. She got hers because the other hens were bullying her and pecking out her feathers. I had to remove her from the flock and treat her wounds with hydrogen peroxide then applied Neosporin. After a month of recouping I reintroduced her to the flock ... well...
This morning when I went to clean the coop, I noticed blood mixed in with the poo. I inspected all my girls and one of my hens did have a dirty butt. Her butt was covered in what looked like broken egg. There was no blood on her. I was able to pick her up and she was pushing out what felt...