It's not in California, but for true shooting summer camp in 2014 (2012 and 2013 are full) try the NRA program here http://www.nrawc.org/adventure/index.html
. Sorry no local Camp Bus service. Looking at the PDF flyer, they teach the kids how to shoot .50 BMG.
You might be able to camp there as a family if space is available. Of course, you would have to see what activities you can do alone. I'd call them and get the scoop if you can get out of CA.
Otherwise some Boy Scouts camps offer shooting, but he would need to join.