You may take a 3-hour bus ride from San José to San Isidro de Pérez Zeledón with MUSOC. The buses leave from San José every hour, starting at 5:30 am and ending at 5:30 pm. When you arrive at the bus terminal in San Isidro, look for Transportes Blanco Bus Station where there are two daily buses to Uvita: at 9:00 am and at 4:00 pm (1,5 hour ride).
For more information about public bus services and conections within Costa Rica, check http://www.thebusschedule.com/cr/