There is one campground located within 30 minutes of the best groves of Bristlecones. It is up at 9200 feet. Bring everything you'll need. There are limited facilities.  

I was not properly adjusted for hiking around at such a high altitude. I left sea level in the morning and was running around at 12,000 feet that night. Altitude sickness can be a real concern when visiting the Bristlecone Pines. Bring plenty of water and go slow. Give your body a chance to adjust to the lack of oxygen before reaching the groves at the highest altitudes. Return to a lower elevation at Lone Pine if you begin to feel funny. Some people stay a night at Mono Lake in order to help acclimate themselves before reaching the highest elevations. 

The full moon was rising the night I arrived. The sky turned shades of purple and pink. The next morning there was a clear sunrise and blue skies. Clouds arrived in time for a colorful sunset that night. This was a memorable trip. I must go again.