You can ask for student discounts on bus fares, but the prices are so low it might not make a difference. Ask about traveling directo (express) so you can avoid multiple stops in small towns.
The currency in Costa Rica is the colon. You might want to get some local currency before you arrive, because the sole ATM at the international airport is difficult to find, in the parking garage!
The dry season (best for travel, but also more expensive) is December through April. There is a little dry season again in June and July, but otherwise it rains a lot between May and November. This makes for lush rainforests but otherwise it can be tough to travel then! The dry season can get hot, up to 90 degrees Fahrenheit.