I have a shower in my RV that I use. Other than that, I don't know of any nearby showers. The Cottonwood campground, which is close by, does not have showers.

That’s it. Or find a truck stop that rents showers.

We were self contained. But I'd check with the visitors center about using the facilities at campgrounds inside the park. Perhaps they have a day-use fee. I'm pretty sure they have shower houses. But I could be all wrong about that. Good luck!

Water is just so precious around the area you do need to leave to either Coachella or Salton Sea (another nice area to visit) If you search Google, you can find some public shower places. It would be less expensive if you purchased a shower bag and take an outdoor shower as long as you are ruffing it. Would cost less than the gas. Just looked up on Amazon for a pop up shower/toilet tent for $35 or so. Enjoy the area, it is a treasure.