YARTS (Yosemite Area Transit) is your answer. They run on weekends in September. So plan for the start or end of your hike to fall on a weekend.
If the start of you hike falls on a weekend: Drive you car to Mammoth Mountain Inn, park there, board the 8 am YARTS bus, arrive in Yosemite Valley Visitors Center at 12:05 pm, eat lunch, take the shuttle to Happy Isles TH and be on your way. This makes the first day a short one, but all you need to do is get 4 miles up the trail to Little Yosemite Valley.
If the end of your hike falls on a weekend: Park at the TH parking lot in Yosemite Valley. Do your hike to Reds Meadow. Take the Reds Meadow Shuttle bus to Mammoth Mountain Inn. Stay the night at the Mountain Inn and the next morning catch the 8 am YARTS bus to Yosemite.
If you don't want to stay at Mammoth Mountain Inn there is a free bus that goes down to Mammoth, and another free bus inside the town of Mammoth. So you can go explore the town after your hike, lots of great food, drink and entertainment. Then stay in a nice hotel and the next morning catch the YARTS bus outside Shilo Inn in the town of Mammoth at 8:30 am.