Since I happen to work in the wastewater treatment field, I would like to point out that, technically, you do not have to bathe in potable water. You can and most folks in the 1st world do, but it is not, strictly speaking, necessary.
I would, however, recommend using potable water for dental hygene.
You may want to distinguish between ‘filtered’ water (as through a brita filter or another carbon filter, for example) and potable (implying sterile) water. Yeah, depending on the components, the cobbled-together carbon filter might (or might not, depending on the assembler!) remove a bunch of contaminants and sediment and the like… but I would still recommend boiling the water before consumption. Also. Depending on the quality of the filter, several passes through the filter may be required to remove the desirable amount of suspended solids.
That filtered water could (depending on the source and the nature of suspended/dissolved contaminants!) be safely used for applications that do not require strict water purity or clarity. Like bathing or washing your clothes.
Also, ya’ll don’t mention it… but you can ‘take a shower’ out of a bucket (5-gal, paint). You can also wash your clothes in a bucket. The water source was a nearby lake, so… yeah. Wash/shower for variable degrees of ‘cleanliness.’ By the way, it’s simple. Clothes + Bucket + Water + Soap [optional] = clean’er’ clothes. Clothes line to dry them on, or a table. Whichever.
Hmm… and since I’m on that track, you can rig up a simple shower with a suspended water-tank, a bit of tubing, a valve (not, strictly speaking, necessary), and a shower head [also not necessary]. Add some power and a waterproof heating element (see every house known to man with hot water) and viola! Warm shower. If you’re curious how much power? Lots. Your car-battery is not going to be enough… unless you’re just splashing yourself with the pan off the stove.
By the way. Water is heavy. So be careful how you keep your tank suspended or it may not stay suspended. Also be careful hooking up your improvised water-heater. As any electrician will tell you : water + electricity = Dwarfy Fun [okay, maybe not dwarfy fun…].
And before you ask : yes. I like commas.