It looks like the first day of fasting is on Tuesday 12 (To be confirmed).
If you're not a Muslim, it is strongly recommended to avoid eating and drinking in public.
Restaurants will have their windows covered, and 85% of the country will be fasting the whole month or, in about 50% of cases, most of it as stipulated by Islamic rules.
Whilst not a lot is likely to happen to people not fasting, it's generally considered extremely rude to eat or drink in public.
I'm unsure how Bali treats fasting but that majority Hindu area likely carries on as usual.