The same thing happened to us. Got my favorite chicken, too. The bobcat will probably be back looking for more to eat. We had a window in our coop and the bobcat knocked out the screen and jumped in and killed two chickens in the middle of the night. We heard the ruckus and went out immediately. We covered the window with half inch hardware cloth secured by big washers and screws and it hasn't been able to get back in there despite several tries over the next couple of weeks, but did come back and killed another hen one late afternoon. I chased it, it dropped the chicken, and like you we ate her. That cat jumped our 7 foot fence with ease! It didn't seem very afraid of us at all.
I'd go ahead and eat your girl. I'm sorry for your loss.
I'd go ahead and eat your girl. I'm sorry for your loss.