Omegared,
My favorite place to camp is called the Freedom Trail head. It is free and only 1.2 miles from the hot springs. There is room enough for 30-40 cars and large semi flat areas to set up tents and equipment. And you do not need a Forest Adventure pass. It is at the same elevation as the Bowen ranch so with the shorter distance it feels like a hard hike for some. It is a beautiful place with many natural wonders.
To get there turn right on the gated dirt road just before you get to the Bowen ranch. Go 3/4 of a mile to another gate and turn left. Go 1.25 miles to the very next left turn and then @ 200 yards for your 3 rd left turn. Then go 1/2 a mile to the parking lot. Look south and east for the trail to the springs.
You may need a high clearance vehicle but I have been seeing many cars make this trip lately as the road has been improving with increased use.
Enjoy and good luck.