This is so simple to build, I have one in my backyard and love it. Make sure you purchase outdoor shower it is quite different than indoor for rust, mold, mildew etc.
I was thinking about this the other day and realized I should have purchased fence material, not real wood, I know it is hard to write. However, you build your base as a wood deck bottom,this is a great drain system we have ferns on the outside bottom,they are huge. Treated outdoor deck boards painted grey matches house.
Use you fence material around this and add the gate. The top is simple board cut for a pergola. I would go to a home depot. I did not put a top, but I did purchase a pergola cloth one for the top. I use the top at the shower. It's brilliant I use the side mosquito white netting on the french doors on the outside on large curtain rods. They are huge and zipper together and also have Velcro to hold to the side of the outside side panels to totally close you in and leave the doors open. Or you can use it around a four poster bed, it is just fun.
Back to the shower the pergolas that are free standing as you are aware are the ones I use on the top of the shower. As the weather cools we sometimes pull it across, run some hot water and tne interior is great, we then roll the top back and secure with velcro rolled up, and held in place with velcro straps to the edge of the corners.

Do the following two items call your plumber so you locate in the right location and 2 go to Home Depot and talk to the fence people and the wood section pre treated.
It takes three days the whole project.
We planted ferns around the outside and they are giant.
It is great when we come home from beach,we just simply keep a vinyl rattan weatherproof chest, it holds a plastic box that has shampoo, soaps in little boxes each named and towels, bathrobes cotton simple, shoe toe sandals to stand in shower in.

On the way into the house, we drop our towels, suits into the laundry and enter wearing robes, rolled up small socks amd slippers are kept by the back door.
We live near the beach and this is the best investment, no sand in the house, all clean up outside. Cost was 1500. materials etc. enjoyed!

Thank. You, I think this will work

Do you have a picture you could send me?

Thanks for the info COConsultants!