If you can add 50 miles to your trip, it might be easier for you to start at Walker Pass, which is 50 trail miles south of KM. You can take a bus to Onyx, then hitch up to Walker Pass. I had a friend meet me at Onyx last year, and I believe he did it all by bus.
Kern County Regional Transit (in Bakersfield) is the bus that services Onyx. You might find their number by doing a web search, or maybe the Onyx store could help you (760-378-2151) or try the Onyx Post Office (760-378-2121). I find that PO personnel in small towns are a wealth of information for hikers.
FYI - in case you haven’t been to KM before, there really isn’t any “there” there. KM is just a store. There are a few ranch houses scattered around, and a restaurant somewhere down the road. But it is by no means a town. Just the one store.
As a final thought - doing the extra 50 miles before KM might help you get your trail legs before you tackle the Sierra.
Good luck.
yogi
yogi