Baths can be unhealthy because when you take a bath all you're doing is washing off the dirt and grime from your body and just sitting in the filth.
However a bath is better than not getting any shower at all.
If I want to take a bath to soak my body in I prefer to take a shower first to wash off any filth and then just soak in a nice warm bath.
If possible the elderly person should bathe every few days.
However if the elderly person is not able to bathe themselves or not able to walk etc then they should bathe at least twice per week.
Even a good sponge bath is better than not bath at all.
If they go longer without bathing then they could have skin breakdowns and infections.
It's okay to not shower for a few days but any longer than that then you can get smelly and it's not good for your health to now shower for longer than a few days.
There's some days I can go a weekend without showering or bathing when I just don't feel like it and I'm not that dirty.
But most days I do shower everyday of the week or I feel terrible and I also have to go to work so I need to shower.
As long as your showering every few days you're doing good.
It's okay to skip a shower for a few days but any longer than that is not good for your health hygiene wise.
Even if you don't smell yourself other people may notice you smelling bad.