Part of the beauty of this national park is its remoteness. But that doesn’t have to mean a long drive. Public shuttles run daily, Memorial Day through Labor Day (note that hazardous road conditions can change scheduling, so check in advance). For a reasonable fee, the Sequoia Shuttle picks up passengers in Visalia, located 35 miles to the west, for the 45-minute drive to the park, passing through the hamlet of Three Rivers then continuing to the Giant Forest Museum.
Once inside the park, you can pick up the park’s free shuttle, which stops at key destinations, such as the General Sherman Tree and Moro Rock. In-park shuttles are in service roughly the same time as the Sequoia Shuttle; during the winter holiday season, service is resumed typically for the last week of December through the first few days of the year, with stops at Wolverton Snowplay Area, the General Sherman Tree, and the Giant Forest Museum. See the park’s park transit page for details.
If you want to go even further with your public transit options, consider using Amtrak. Trains stop in the Central Valley town of Hanford, then Amtrak buses continue the 35 miles east to Visalia, where you can pick up the Sequoia Shuttle to get to the park.