Stephan:
I'm not aware of any campgrounds that meet your requirements. I agree with your desire to sleep a little high to acclimatize. I believe that the best place to sleep is the highest altitude at which you don't get sick.
If you insist on sleeping near Reno, I would drive up the Mt. Rose highway towards Lake Tahoe. There is paved parking for the Mt. Rose Trail on your right at the highest part of that highway. I think you could park there overnight. There used to be a campground across the highway from the trailhead; I don't know its status and that may be the one you said was closed. This spot is close to Reno, but it's not on the way to Whitney. The authorities might hassle you if you slept in the car or set up a tent, but I think you would be OK if you found a secluded spot for your bivy away from the road.
I would suggest Conway Summit, about half way between Bridgeport and Lee Vining. It's a good two hours from Reno, but it's right on your way to Whitney. I've been known to sleep in my car behind the maintenance building (on the left, probably not legal). I've also driven up a dirt road on the left to sleep. In the summer, you can drive up the paved road on the right towards Virginia Lakes. This will take you to almost 10,000 feet. There are several turnouts along the road and a trailhead at the end. I think there is a campground in the area, but I'm not sure. Again, I wouldn't suggest setting up a tent anywhere other than a campground, but I don't think anybody would bother you if you slept in your car or threw a bivy on the ground next to your car.
Feel free to post more questions if you have any.
Bob
