The plan will be more like - park in the Valley, get on the bus, ride to Mammoth, spend the night, get on a shuttle, get on another shuttle and get off at the trailhead.
You could catch a ride with someone heading over Tioga... might be able to hook up with someone via the forum who's heading to the east side on the same schedule. But you might have to add a day to your travel time on either end depending.
You could park in Mammoth, YARTS to Yosemite and start from that end instead - would reverse the bus schedule and not leave you with those shuttle rides in Mammoth until you got there. The last shuttle out of Reds Meadow leaves fairly late in the day, after 5 I think.
