No, there is no specific dress code at IIT Bombay and you are free to wear whatever you feel comfortable with. There are people who wear shorts, jeans and even pants. All you have to make sure of is that you are feeling comfortable and following the ethics.
One of my friends used to wear shorts throughout his college life and just wore jeans during his Mechanical workshops. So there are no boundaries to adhere to any dress code at IIT Bombay.