Korean national health insurance does not cover treatment in Indonesia. Comprehensive travel insurance with medical evacuation cover is essential — serious cases are usually flown to Singapore.
Read the motorcycle clause: most policies only cover scooter injuries if you hold the correct motorcycle licence plus an international driving permit, and wore a helmet.
Bali's dry season is April to October. Seollal, Chuseok, the late-July to August summer holidays and the Christmas period are the peaks; April, May, September and early October are the value windows.