I have never had a problem hitching from a major trailhead down to 395 where you can pick up the CREST bus, even when I'm stinky and dirty. By major trailhead, I mean any of those where the permits are usually fully subscribed, like Cottonwood, Whitney Portal, Kearsarge, North Lake, South Lake. I wouldn't count on it at Shepherd Pass or some of the others that don't get much use. I can usually get a ride down the hill within five minutes; I don't think I've ever waited more than 45 minutes, even late in September when things are much quieter than in July and August.
As to hitching uphill from 395 to a major trailhead, I've found it works better in the morning than in the evening. I once waited for nearly two hours to get to Cottonwood trailhead from Lone Pine, but that was in the evening and it was late in the season after the pack station there had already closed. Mornings during July and August shouldn't take more than 20 or 30 minutes.
You can legally park for over a week in the public lot behind the police station in Bishop. (OK'ed by Bishop Police as recently as 2010.. I've done numerous trips using this configuration -- park in Bishop, CREST south to Lone Pine, hitch to Cottonwood trailhead, hike to North Lake or South Lake trailhead, hitch back down to Bishop.