Biswas was born in Nalbari, Assam, to Bengali Parents Jagdish Biswas and Meera Biswas. Her mother, an early influence, was a history Teacher and a pioneering figure for female theatre artistes in Assam; and she came into contact with artists like Bhupen Hazarika, Phani Sarma and Bishnuprasad Rabha early in life. She studied Political Science at Nalbari College, and later joined the National School of Drama, New Delhi.After graduating from NSD in 1984, she joined the NSD Repertory Company.