Not sure if the bus dates work for you, but here's some research info. I've collected for my HST trip planning. Since I have not used any of the services I'm recommending, you should verify all the information for yourself.
1) Greyhound to Visalia, CA
1a. Greyhound: 425 E. OAK Ave., Visalia, CA 93292
2) Sierra Shuttle from Visalia Convention Center to Sequoia National Park's Giant Forest Museum ($10/person).
2a.
http://www.sequoiashuttle.com/en/routes.php 2b. Tel: 877-287-4453
2c. 5 departures between 7:00AM – 1:00PM
2d. ~ 2.25 hr drive
2e. Convention Center: 303 E Acequia Ave, Visalia, CA 93291
3) Use Sequoia Nat'l Park internal shuttle to Lodgepole to pick up permits. Shuttle buses are free.
4) After hike, camp at Whitney Portal.
5) Next morning, have Bob shuttle group from Whitney Portal to Lone Pine.
5a. Tel: (760) 876 1915 for a quote and reservations.
5b. Note: Call Bob prior to starting hike to confirm. It’s alright to deviate from schedule, so Bob will provide his cell number to call. The Whitney Portal Store has a free land line to call with.
6) Catch Crest Bus from Lone Pine to City Hall in Ridgecrest ($15).
6a. Tel: 760-872-1901
6b. Operates only M, W, F
6c. Departs Lone Pine 10:25AM; arrives 11:45AM at Ridgecrest City Hall.
6d. Bus stop located at Statham Hall (138 N. Jackson Street, Lone Pine, CA)
7) Rent car from Avis, next to City Hall to drive back to Los Angeles
7a. Avis (760-446-5556): 901 N China Lake Blvd, Ridgecrest, CA 93555
7b. Mon-Fri: 07:00 AM-06:00 PM, Sat-Sun: 09:00 AM-04:00 PM
Good luck!
Tung