Bandages don't usually stay on long, though for tonight, hopefully it'll be fine. She might be getting pecked on more because she's different. What breed is she? Some breeds are more aggressive (I think some Leghorns are, like the Whites) than others. I think adding more perches would be better...
I wouldn't call that a serious cut, though left untreated, it could become serious. Clean it with a saline rinse (or something similar if you don't have it) and put neosporin or bag balm on it. If you can, I would separate her into a clean kennel where you can clean up any poop so she doesn't...