I was just in that area a week ago. Sabrina, where I stayed, is now closed for winter. It was 18 degrees the night I was there and the camp host was already gone.
Current concessionaire for Bishop Creek area is Recreation Resource Management.
http://camprrm.com/2009/03/bishop-creek-campgrounds/ You can "like" them on Facebook and see their updates.
Another Inyo concessionaire,
CLM Services, publishes e-mail newsletters with updates for each area. There is a map on their website. At the bottom right of their home page there is a link to the newsletter list; you check off the ones you want and give them an e-mail address for a free subscription. Here is their Inyo NF page:
http://www.clm-services.com/inyo-national-forestI had a long chat with a camp manager (not a host, a manager of multiple camps) a couple of weeks ago. Concessionaire services are contracted for the season and for a specific amount. The concessionaire pays the USFS that amount or does an equivalent amount maintenance and upgrade work on the managed facilities. The concessionaire pays its employees.
Re the White Mountains: I don't think that boondocking is allowed; cannot check because USFS website is shut down. Grandview (free) is it. That is a LONG drive from Bishop Creek.