The Carson River resort campground on the river is unimproved, with no facilities at all.
There are several locations upstream that are public and free.
Almost all of the USFS camps will be closed by 10/15. There is a BLM campground on Indian creek reservoir that has showers, but I expect they will be closing in mid October too.
Wolf creek campground further upstream has bathrooms, but no way to lock the public out. I don't know how they close it, except locking the door to the shitter.
BMW Motorrad USA customer service: "We make superior motorcycles and continue to improve them."