"You are lucky to be that close to Sturgis when this rally is going on. "
There are camsites for millions. I have never had a reservation in 9 trips to Sturgis and never had a problem getting a campsite right in town.
On the west side of town, at the Route 90 exit there is a campground named Day's End. They always have space for a bike and a tent. The showers are private and clean.
How long a queue at the showers?