JerLund,
I can't speak from experience, but I've done a ton of research(mostly because of this addictive messageboard!!!)
Try this link.
http://pub4.caso.ca.blm.gov/bishop/tuttle.htmlFrom what I hear Tuttle Creek campground is down the canyon at 5,000ft and is rarely full. I'm planning on camping there the night after our climb in Sept. I believe there is a Lone Pine campground as well a bit closer to town.
However, I believe there are about 16 non-reservable spots at Whitney Portal specifically for Whitney hikers. So if you get there early you might be OK.
Good luck and Happy Trails
