Bajpaie was brought up in Santiniketan, West Bengal, India. She spent her childhood at Patha Bhavan School there, and finished her MA in English Literature from Visva Bharati University. Both of her parents were professors of political science at the University of North Bengal. She took her first lessons in music from her father, Bimal Bajpaie and learned to sing at the age of three. Later she started taking learning from eminent musicians of Santiniketan like Bijoy Sinha, Chitra Roy, Shyamali Banerjee, Chandan Munshi, Madhumita Roy and Mita Haque and received training in Indian classical music and Rabindra Sangeet. In 2005, Bajpaie joined BRAC University in Dhaka as a lecturer in English. In May 2008, she left for London, to pursue another MA degree in South Asian studies at the SOAS, University of London.
By the age of 3, she started singing. She released her debut album Notun Kore Pabo Bole in 2007, which was a collection of Rabindra Sangeet. Her second album Shikawr released in 2014 with several musicians from West Bengal. Sahana’s second Rabindra Sangeet album Ja Bolo Tai Bolo was released in 2015 and the latest solo album, Mon Bandhibi Kemone in 2016.
Since her music career Bajpaie released two Rabindra Sangeet albums. Notun Kore Pabo Bole was her debut album which was released on 6 March 2007, from Bengal Music Company, Dhaka. The album contained representation and arrangement of Tagore-songs.
She released her second Rabindra Sangeet album Ja Bolo Tai Bolo in September, 2015 in India and Bangladesh, which contained a collection of devotional and folk songs of Tagore.
Her third solo album Mon Bandhibi Kemone released in 2016, was a collection of folk songs of Bengal, which Bajpaie and her associates had collected and arranged them in a contemporary format. Music arrangement of this album was done by Samantak Sinha and Satyaki Banerjee.
In 2012, she made her first playback in the Indian Bengali fantasy film Tasher Desh. In 2013, Bengali comedy film Hawa Bodol which was directed by Parambrata Chattopadhyay. In 2016, she made a playback for the Bengali film Under Construction, and sang for Family Album by Mainak Bhaumik, which was a tune by Anupam Roy. In 2018, she sang for two films Ek Je Chhilo Raja, a film by Srijit Mukherjeeand Rainbow Jelly, by Soukarya Ghosal. More recently, in the Shiboprasad and Nandita directed, Kontho, she sang the song, Shawbai Chup.
In 2001, Bajpaie married her childhood friend Shayan Chowdhury Arnob, a Bengali musician, singer-songwriter and composer. They got divorced in 2008. She now resides in London, where she serves as a senior teaching fellow in Bengali in the Department of the Languages and Cultures of South Asia at SOAS South Asia Institute. She is however currently, on leave, pursuing her PhD in ethnomusicology at King’s College London. Later she married Richard Herrett and the couple have a daughter name Rohini Herrett.