Do old people bathe regularly?

Depends on the geezer.

I don't see why they wouldn't, unless they had a disability that prevented them from doing so without help, and had no one to help them.

Most of them do more than younger people. All the older people I ever met have a routine to bathe every day

I think most do as they really don’t have anything better to do.

Sometimes when people smell, it's that they don't wash their clothes, or leave them crumpled and wet after washing so that mildew sets in before they manage to dry. Hauling loads of washing into and out of a machine and on a clothes horse or a line is quite physically demanding for people who don't have a lot of strength. For me it's a full-on activity and not just a five-minute chore like emptying the dishwasher.

You took the time to define regular!

What's old?