As with the whole of India, only drink bottled water and use it when you're cleaning your teeth. I kept a bottle with a bit of water in it beside the sink so as to remind myself to use it. Also, avoid ice and salads as they will probably have been washed in dodgy water. Its all common sense really but if you stick to it, you limit the chances of getting ill. A litre of water only costs from between Rs10 and Rs15 so its cheap and available everywhere.
Water is not for drinking although it would be strangely bizarre if you would even think of brushing your teeth with mineral water. The tap water taste rather like a poor mix of salt water. Mineral water is available very cheaply and most places do not provide ice which is a relief in one way, but in another - not the coolest drink you can get.
Clean drinking water, these days, is not too difficult since bottled water is sold in most places. In the past, rumors of bottled water refilled from local taps and resold were common enough but these days bottled water is a fairly mature industry and supplies seem reliable. Check the seal, and see if things are floating in it before buying. A certain amount of suspicion can be healthy.
You may sometimes encounter backpackers who drink the local water everywhere and claim no ill effects. Whether this is because they have an unusually robust intestinal tract or because they have not yet encountered anything serious, it's hard to say. Some travelers swear by papaya or yogurt (recommended - eating both regularly helps your digestive system) and others rely on the powers of gurus, gods, or fate. One young woman was going high tech, with a battery device that sent current through her body to purify her gut.
Two things to be absolutely careful of in Bombay: The water and the roads. Drink only bottled water; costs around USD 0.25 for a one litre bottle. If travelling by road, be careful of the speed breakers. If you do manage to survive them, the potholes will surely get you! Jokes apart, it is a good practice to drive slowly in Bombay, especially at night.