I would not bathe her. Lying on a warm towel would be good for her. Here is some more info about tube feeding:
https://www.backyardchickens.com/threads/go-team-tube-feeding-updated-12-29-2019.805728/
https://www.backyardchickens.com/threads/go-team-tube-feeding-updated-12-29-2019.805728/
Hens go broody when you don’t want them to… and won’t go broody when you do.

