A simple segment goes from Yosemite to the Mammoth area, as far south as Red's Meadows.
There is a bus transport from yos to Mammoth Mountain Inn during the summer, and you can do that segment with the bus making it a loop. I've done it, and recommend it.
South of there, it becomes more problematic.
I did a loop from Vermillion to Reds, then looped back along another trail. Nice trip, recommended.
People do various loops from Vermillion to Florence Lake, also recommended.
South of Florence, it starts to be a tougher logistic problem, as you start on the west, end up on the east.....which is the problem for the trail as a whole.
Eastside public transport is problematic.
Westside public transport is problematic, except for the Yos shuttle, and AMTRAK into Yos valley (which I've taken, and is great)
