Yes, Costa Rica has its own public transportation with many private bus companies offering to take you all over the country. Many of the buses have fixed schedules to the major cities and towns.
Getting to the smaller towns is a bit of a challenge but with a little ingenuity and patience, you can do it. Most tourists who decide to tour the area to the more remote locations opt to rent a car. It is by far the easiest way to get around if going off the beaten path.
Interbus ► https://www.interbusonline.com/home/home.asp
Tica Bus ► http://www.ticabus.com/esp/
Grayline ► http://www.grayline.com/Liberia_Guanacaste
Nica Bus ► http://nuevo.transnica.com/
Public Bus Schedules ► http://www.liberiacostaricainfo.com/BusScheduleLiberiaCostaRica.html