The problem is that you intend to end at Roads End, and it is difficult to hitch a ride from there all the way out to Hwy 99, then north, then across the Sierras at Tioga Pass, then north again to Bridgeport and Twin Lakes.
Instead, if you don't exactly end at Roads End, and you head out and over Kearsarge Pass, which brings you to Onion Valley. From there, you ought to be able to hitch a ride down to Independence. From there on the East Side, you can hitch or bus up to Bridgeport.
–B.G.–