Map from Google - Mumbai

In Mumbai (formerly Bombay), the capital of the state of Maharashtra, the climate is tropical, hot all year round, with a long dry and sunny season from early or mid-October to early June, and a rainy season, due to the south-west monsoon, from June to September or early October, characterized by a stuffy weather, cloud cover and frequent rains, which occur almost every day and are sometimes torrential.
In the pre-monsoon period, from March to May, the heat becomes intense, so that sometimes temperatures can reach 38/40 °C; this happens partly also in the period after the monsoon, in October and November, when they can reach 36/38 °C.
In winter, from December to February, the weather is nice and it is hot during the day, sometimes very hot (temperatures can touch 35/36 degrees), but at night they normally return below 20 °C, and from time to time they can go below 15 °C: it is better to bring a sweatshirt for safety.
Here are the average temperatures.
Average temperatures - Mumbai
MumbaiJanFebMarAprMayJunJulAugSepOctNovDec
MumbaiJFMAMJJASOND
Min (°C)171821242626252524232118
Max (°C)313133333332303030333432

As mentioned, the monsoon in Mumbai lasts from June to early October, and is intense since the wet currents come directly from the sea: in July 800 millimetres of rain fall. In July and August, the weather is almost always cloudy and air humidity very high, although the sea breeze gives a bit of relief. In Mumbai, rainfall amounts to about 2,250 mm per year.
Here is the average precipitation.
Average precipitation - Mumbai
MumbaiJanFebMarAprMayJunJulAugSepOctNovDecYear
MumbaiJFMAMJJASONDY
Prec. (mm)110115525800530310551552260
Days000011523211431078

In theory, from May to November Mumbai may be affected by tropical cyclones, although they generally affect the areas to the northwest and to the south of the city (or at least that is what happened over the last decades); the fact remains that the city can be affected by a cyclone at some distance, with heavy rains, as happened with Phyan in November 2009.

Mumbai

The Arabian Sea is warm enough for swimming throughout the year, as you can see in the following table.
Sea temperature - Mumbai
MumbaiJanFebMarAprMayJunJulAugSepOctNovDec
MumbaiJFMAMJJASOND
Sea (°C)262526272929292828292826