If a shower is your limiting criteria, you have limited choices to being with. Here is a list of the campgrounds. If you click on each one it lists the services available.
http://www.fs.usda.gov/activity/ocal...32295&actid=29
If none of the ones with showers are on/close to your route, you might have to make a compromise. As for general gun season, when dispersed camping is generally not allowed, you can always call the U.S.F.S. to find out when that is.