Costa Rica's volcanic terrain and dense trail networks make it genuinely good mountain biking country. The area around Tilarán and the shores of Lake Arenal is the best-established riding region, with routes ranging from mellow lakeside tracks to steep singletrack through cloud forest. Rides here can run from a couple of hours to a full day.
The Central Valley around San José offers easier access and well-maintained trails through coffee plantations and along river valleys. For something wilder, the Osa Peninsula has rough tracks through rainforest, though mud is a constant companion in the wet season.
You can rent decent bikes in Tilarán, La Fortuna, and Monteverde. Guided rides are worth considering for backcountry routes where navigation is tricky and mechanical help is far away. The dry season (December to April) is the most comfortable time to ride, though the green season brings emptier trails and dramatic scenery.