You might be better off getting a pump up sprayer from a home center, splice on a kitchen sink spray wand, paint it black fill it with water and put it in the sun. Shower before sundown or the water will get cold. You can shower in the open if you wear a bathing suit. See if a friend has a tent, pad, and sleeping bag you can borrow.
On the bathroom, bring a small shovel, toilet paper, and some hiking shoes. Go for a walk with paper and shovel, dig a hole, drop your drawers and squat above the hole. Nothing quite like having a cool breeze blow up your butt. The other option which may be better is poop in a garbage bag. Walmart sells folding toilet seats in the camping department. The bathroom would be the tent.