The Hinoki Stool from Design Within Reach is exactly what you are looking for — but expensive at $300. It's made of Japanese cedar and is the same kind of stool used in Japanese saunas. We found some other cedar and teak options but many were folding, which didn't seam stable in a shower.
If you have a tub, you could use the Hinoki Tub Bench, made from the same rot-resistant cedar, which is only $100.
Anyone have alternative ideas?