Blkdimond17, Never done Ritter in winter so bear with me. FWIW, Backcountry Skiing California's Eastern Sierra shows approaching the Shadow Creek drainage from the Minaret Picnic Area (the start being the Main Lodge at Mammoth Mountain), pgs. 128-130, 1st edition. The route description is too much to type here. Stats per the book: Trailhead elevation: 8,900', Vertical Descent: 3,000', Ski/SS/Hiking Distance: 11.5 miles. Per the book: "It is also possible to access the south side of Mt. Ritter from the June Lake Loop. While the distance is shorter, it involves gaining and losing more elevation."
Paul Richins, Jr.'s book 50 Classic Backcountry Ski and Snowboard Summits in California section info on Mt. Ritter shows the approach to Shadow Creek from Agnew Meadows (pg. 118-120). Stat per the book: 12 miles