I'm a bit late coming in on this one, but I've been coming across from London (England) to hike various areas in the Sierra for a few years. We have tried various routes including the old Greyhound overnighter to Reno years ago, vans from variosu pack companies, car hire etc. Last trip we discovered that we can fly direct to InyoKern airport, near Ridgecrest, directly from LAX. Its a regular shuttle and there is also an Avis car hir facility there, or you can get a ride into Ridegcrest. I think there maybe other flights out to other airports, but I haven't checked these out.
This means that I can actually leave London at 10am, arrive LAX 1pm, make Inyo-Kern by 6pm, pick up a car and make it to Bishop by nightfall.
You might want to check out the flights from Inyo-Kern as it'll save you being hit by a one-way hire cost and its a lot quicker.
Airport site with details of flights in at:
http://www.inyokernairport.com/Enjoy the JMT; I'm heading into the Kaweah this year to do an 8 day circuit...I've seen them from Whitney so many times and thought this was the year to check them out for real.