Lol. Good luck with that! BV is so damn busy all summer any more. If you want to get a dispersed camping site anywhere near BV for Independence Day weekend I would suggest arriving today or tomorrow. Everything, and I mean EVERYTHING will be full this weekend....
That said, only the developed campgrounds within the AHRA require a reservation. Options for dispersed camping include Stone Cabin, Rapid #4, Rapid #5.5, Rapid #6, Elephant Rock, Tunnel View, Turtle Rock and all of Fourmile Recreation Area. There is also dispersed camping available above Cottonwood Lake and in multiple spots along the Cottonwood Pass road, also up North Cottonwood.