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
I've climbed Ritter in the winter from the rush creek hydro power station on the June Lake loop. Ascend the tramway (technically not kosher I think, but I know lots of people do it), hike above north shore of Agnew Lake, cross over by the dam to counter around south shore of Gem Lake and then climb up to Clark Lakes. Descend to Badger Lakes and then up to the outlet of Garnet Lake. Beautiful ski/hike across the Garnet Lake basin, then climb over the 3200m+ col to Nydiver Lakes (I camped on the high bench above the lakes here). The climb up to the SE snowfield ("glacier") of Ritter from here or to the Banner/Ritter Saddle is straightforward. This route is shorter by about two miles, but as noted above it involves a lower trailhead and a bit more up and down than the "normal" route from Minret Summit/Shadow/Ediza. The June Lake approach involves about 1900' more climbing.