Andy, the Wilderness Permit Office number within Inyo National Forest rings in the White Mountain ranger station in Bishop, but it's not their direct line number. It's shown at the bottom of this web page: Wilderness Permits - Planning Your Trip:
Still have questions about wilderness permits?
Call Inyo National Forest for wilderness and permit information(760) 873-2483 Open 8am to 4:30.
Winter season: closed on weekends and holidays.
May 15 through Oct 15: open every day.

For Mountaineers Route info:  some of the links on this page are aged or missing, but there are quite a few that still good. It's the top of the "important Link", top of the Reference forum: Mountaneers Route info and links