Bali's tap water isn't run through the kind of treatment and pipe system that makes it safe to drink straight from the tap, in a rental villa, hotel, or local home. This is true island wide, not just in less developed areas. Boiling water for a few minutes kills the bacteria and parasites that cause most stomach illness here, and it's the simplest fix if you don't have a filter or bottled supply on hand. Bathing and showering in tap water is fine for babies and kids: skin contact isn't the risk, swallowing it is.
For daily use, keep a stock of large refillable water jugs (common in most Bali kitchens, delivered by local water companies) or bottled water, and use that for drinking, mixing baby formula, making ice, and rinsing toothbrushes after brushing. Many families also install a simple countertop or under sink filter once they're settled in for a longer stay, which cuts down on plastic and delivery runs. Wash fruit and vegetables in tap water if you like, but a quick rinse in filtered or boiled water afterward is a good habit for babies just starting solids. Restaurants and cafes aimed at tourists and expats generally use filtered or bottled water for ice and cooking, but it's worth asking if you're ever unsure, especially for very young babies.
If your child does end up with a stomach bug, mild diarrhea or vomiting for a day or so is common as kids adjust and usually clears up with rest, breast milk or formula, and oral rehydration solution. Watch for signs of dehydration: fewer wet diapers, no tears when crying, unusual drowsiness, or a sunken soft spot in babies, and treat those as reasons to act quickly rather than wait it out. For babies under a few months old, or if symptoms last more than a day or two, come with fever, or you're at all worried, see a doctor or clinic rather than guessing. Bali has pediatric clinics and hospitals used to treating both locals and international families, and getting checked early is always the safer call.
This is general information, not medical advice. For anything specific to your child, please consult a doctor or a travel-health clinic.
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