That's a good question. www.rome2rio.com is my go-to site for public transit, but even it doesn't have an option that doesn't require a car. The YARTS bus serves Groveland this time of year - goes between Sonora and Yosemite Valley, but you'd have to get to Sonora to pick it up.
There is an Amtrak/YARTS combo that would get you to Yosemite Valley. It is via Merced - doesn't pass through Groveland, but once in Yosemite Valley, you could catch another YARTS bus over to Groveland.