Which Kennedy Meadows? There are two.
The northern one is easier to access. You could fly into South Lake Tahoe and see if there is a bus down the east side of the mountains to Bridgeport, then hitch to Kennedy Meadows North.
The southern KM is out in the middle of nowhere. I’d go to Walker Pass instead, it’s only a couple of days south and the road out of Bakersfield would probably be easier to get a ride than the road out of Inyokern.
There isn’t really an official shuttle network on the PCT like the AT. You might put out a request on PCT-l and elsewhere and hope for a response.
As to starting dates - the Sierras are generally mostly snow-free by July. Thruhikers go through earlier, but then have to deal with snowy passes and snowmelt streams. Bugs are a problem right after snowmelt - but less so later in the summer. It will be hot in northern California - so you could set up your hike to end at Seiad in early September if that works for you.
Ginny