The tap water is fine to drink, but can be unpleasant in places (where even the locals often resort to bottled water).
According to the CDC tap water is generally not safe for consumption.
According to the Numbeo water drinkability and accessibility index, tap water has a score of 54.55 / 100 (100 being best).
Numbeo considers this score to be "Moderate"
1 adult could save about 1314$ per year in Bahamas by drinking tap water instead of buying bottled water.
๐ณ Drinking tap water would also help with reducing your plastic footprint and improve environmental pollution.
Like in most countries, water quality and accessibility differs from location to location, therefore it's the best to check the information available on that place.