I couldn't resist looking up what bathing actually does to the bacteria on/in your skin. This rather old paper from 1970 says:
AEROBIC BACTERIAL COUNTS ON HUMAN SKIN
AFTER BATHING
R. J. HOLT
"It may be significant that in some experiments reported above the total bacterial count 10-24 hr after the wash was considerably higher than the pre-wash count."
Seems it was well-known back then from teaching laboratories (where I assume they grew cultures from swabs taken from a hand before and after scrubbing) that scrubbed hands grow MORE colonies!
In a swimming pool or hot tub, most places take regular water samples. In a familial shared bath, I would assume (not a bacteriologist, any out there?) that you would share skin bacteria with your family anyway, plus unlike a swimming pool, the water hasn't been sat there for hours anyway. And unless you make your tea with the remaining hot water afterwards....................
Other work (okay I'm getting obsessed now!), showed that the more bathers, the more bacteria in the bath water (Construction of a leftover bath water model for microbial testing, Sumitomo et al., 2006 -- perhaps from Japan, where they didn't seem to have a problem finding 28 families who shared bathing water).
So, washing generates more bacteria on your skin, you can never get really clean..................
..............and then I finished up with a Mythbusters classic:
www.discovery.com/tv-shows/mythbusters/mythbusters-database/fecal-matter-on-toothbrush/
Some people are obviously never going to go near the bathroom again after this!