What does it cost to have someone come to home?

First, will this elderly person accept a stranger helping her or him to bathe? Many will not.

Second, have you tried no rinse products? They're much safer than showers or baths and don't require stripping down. The person can "bathe" when comfortably sitting down and almost fully clothed. The fall risk as well as the chill of removing clothing in a bath in my mind vitiate the need for showers.

Third, this person's doctor can script for home health care, along with physical, occupational and nursing care, if the need justifies it.

The OP wants someone else to come to the older person's home to assist with showering/bathing. I misread the headline at first too!

I misread the OP and thus removed my earlier statement. 

Our local hospital has a staff of shower attendants that make home visits. They work out of the department that staffs in home nursing, physical therapists, o.c. therapists, etc. I believe they are less costly compared to a caregiving agency.

Call a care agency in your area and ask. Some on here talk about day cares where they can get a bath. I'm not sure how that works. My aunt has home health and an aid comes and baths her twice a week. If your elder lives with you or you with elder, they might not qualify for home health. My aunt lives alone. But you could go on Medicare website and look up home health in your area by zip code. Choose one that has a good score and call and discuss it with them. Your elders doctor would have to sign an order but that is usually not a problem.
If your elder has mobility problems, tell the dr you would like them to have physical therapy for balance and that would help as well. 
If you can get home health through Medicare there is no charge.