I don't.
Really, I don't.
Ok, I do...but not as often as you.
As I mentioned, I visit friends and family often, wherever I go, and I most often stay in an apartment in Oregon, so I shower in houses.
Even when I do stay indoors and I have access to a shower, quite often I will soak a small washcloth and squirt liquid soap onto said washcloth and proceed to wash my body with said soapy washcloth.
This can happen in my van, in a public bathroom, or anywhere really. Even when I'm traveling for work and I'm put in the fanciest hotels, I will sometimes still wash my body like this instead of using the nice, warm, fancy shower. It's just how I roll.
I think it even cleans my body more effectively than a shower. Usually in a shower I will just scrub with my soapy hands instead of using the more abrasive and effective washcloth.
Additionally, there are many public facilities where free showers can happen: public pools, beaches, and sometimes outside of hotel pools.
There are also the good ol' monthly memberships, of which I have not yet surrendered to: YMCA's, gyms, etc.
Where do you shower when you're on the road?
Feel free to share your secrets with me and anyone else who may stop by this site for help!