In reply to Tru:
Hi Tru,
If you don't rent a car you have 2 options; buses or hitching.
I have hitched in the area (with my wife) a few times now and found it pretty straightforward. At least away from the big cities anyway. The towns on the 395 up Owens Valley (Bishop, Lone Pine, Independance, Mammoth Lakes, Lee Vining) should all be ok for hitching. Also Tuolumne Meadows on Tioga Pass Road(which I recommend as a wonderful area and has a campsite, cafe and gear shop) should be good for hitching too, possibly also for picking up climbing partners. Although I guess Yosemite valley itself will be the best spot for meeting climbers as it's the busiest.
In the US, public transport like buses are pretty hard to come by and climbing venues tend to be out of the way from the bus networks. Amtrak and Greyhound do run buses though from the cities to Yosemite. So that would be a good way to get there initially.
My first option though if you can do it is to rent a car. Everything in the US is designed around the car and it will enable you to do more in the time available.
That said if you choose to bus/ hitch you will likely have a great adventure and meet lots of interesting dudes. We haven't really had a bad hitching experience in our year's of hiking / climbing trips out there. We find a succesful tactic is to talk to people at a campsite, cafe, trail, climbing crag and ask for lifts in person. That's a quicker tactic if you can do it than standing at the side of roads. But obviously be careful and be prepared to say no to an offer of a lift if you have doubts.
I should say also that September is possibly my favourite time in the Sierra area. Quieter, warm days and cold nights. I am envious- have a great trip whatever you decide !
Brian