Searching for 'bathing registers' revealed this listing from The National Archives' catalog, describing part of RG 173 from the Suffolk Record Office, Ipswich Branch:
173 - Suffolk Record Office, Ipswich Branch
ID 411 - BLYTHBURGH AND DISTRICT HOSPITAL
ID 411/B - INMATES' AND PATIENTS' RECORDS
ID 411/B7 Bathing registers
Volumes showing dates when each inmate was bathed
A search result from the Internet Archive mentions bathing registers in summary reports about schools in Germany and Holland -- listing when the resident students bathed (see Report of the Education Committee of the London County Council submitting a report of the council's officers on bathing arrangements in schools in Germany and Holland ...).
No. 8. — Each class must keep a bathing register in which the bathing
attendant notes the number of baths given to each class per week. On
the last school day of every month all the bathing registers are to be
submitted to the headmaster. The school doctor is also requested to
inspect the bathing registers from time to time. Three times a year
the headmaster must send in a report to the school authorities,
shewing clearly how many pupils have reported themselves for bathing,
how many have actually bathed, and how many absences have occurred,
together with the reasons for the same.