I know some about that route.  Having recently been up and down it twice on
my way to the dentist..But that's another story...

  Dunno what 'style' camping you may be looking for but a few of the
possibilities are:  Red Rock Canyon SP, about 30miles north of Mojave, if
you go that way.  Dry desert but scenic and they have shade structures and
showers (I think).  Near there is Jawbone OHV area, where you can primitive
camp wherever for free.  Showers at the headquarters station.
  Truckers and some RVs use 'downtown' Olancha's trees as a parking area,
roadside.  Not camping but ok for some sleep.  There are two Rest Stops,
also out there..
  Further north near Independence I've seen a Forest Ser. "camping"  sign.
Big Pine, there is another, also a city park where you can camp informally.
There is an artificial lake park along there, also..Forget the name, but I
see lots of RVs and tents using that one..swimming, too (if you are brave?)
You will spot that  one, it does stand out some...
  Around Bishop, there are tons of spots...Mill Creek County park is one, to
the north but still below the big grade.  Haven't camped at these, myself,
but I am always on the lookout and note likely places for the future..
  Once you climb out of the Owens Valley headed north, you are into forest
service land mostly and you will now be cool..
  From limited experience (a couple of  side trips on my bicycle) along the
Owens valley, the side roads showing camping..there will usually be a low
camp and then as you get to the ends of those roads, many camp sites...but
plan to climb 3-4K feet in elevation to reach the upper camps...Tough in a
Vanagon..easier on a bike...(Hmmm....)
  Have fun, that is a beautiful drive along the backside of the Sierras..
  Don Hanson