I grew up in Mumbai, and depending upon why you are visiting, end November to mid March is ideal to visit Mumbai...no too hot weatherwise. If you are into festivals, then Diwali, the festival of lights is on November 7th and Holi, the festival of color is on 15th March..However, assuming you are also planning to walk around Colaba and other parts such as the Thieves Market or take a trip to the Elephanta Caves, its better to come in the winter months. If you have more questions, email let me know :)
Have a nice day!
India is country of festivals, all the year round.
If you are looking for less excitement between the crowds and want to see Mumbai city as a busy city, best time could be January End till Beginning of April.
Summers arrives by the close of April and then there are Monsoons thereafter which doesn't permits tourists to tour the city freely.
Please check the time of festivals that suits your interests that is Navratra - October and November. You can even try Christmas and New Year Eve. Mumbai is nice to the close of the year.