We strongly advise that you do not travel without insurance. Emergency care can become expensive really quickly. Do check your coverage before you travel as some policies do not cover injuries caused by certain activities such as trekking, scuba diving, or paragliding. Often, if you pay your travel expenses with your credit card, travel insurance is included. You can check with your credit card company for details
If a family member needs special medication, avoid immigration questions by bringing a letter of the doctor and keeping the medication in its original package. There are several pharmacy chains operating in Bali which do give a good service and know what they are doing. Medicine is often very cheap compared to other countries.
Bali has well-equipped hospitals and emergency doctors, located primarily in the south. In case of an emergency, staying in a more remote area can become a real challenge. Vaccination is not required but recommended in some situations