Above Mammoth toward the Mary Lakes area (Duck Pass) there are a number of CG's. I assume you have wheels to get around with. Up out of Bridgeport, which is half an hour north of Lee Vining, Twin Lakes area, never been there though, may have showers as there is at least one resort up there, assume they would rent showers. On your way south on your trip, you can stop at the gas stations and ask about facilities in Bridgeport. Great burgers in Bridgeport or the Whoa Nellie Deli (Mobil station) up the Tioga Pass road a quarter mile, just south of Lee Vining. You may be able to get showers at Silver Lake in the June Lake area. There are spots to camp across the road from the TH, they have water and toliets, may have to hit up the resorts for a shower, not sure. Enjoy all the snow. You did read Wandering Daisies report, right?