Bajpai is a Fulbright visiting lecturer and is currently teaching a course on child rights and laws from international and comparative perspectives, at the Washington College of Law, American University. In India, she is a reader at the Tata Institute of Social Sciences, Mumbai. She was formerly a professor at the National Law School of India University.

Bajpai holds a Ph.D. in law with specialization in child rights and laws and has been involved in teaching, research, training law reform, legislative drafting, and consultancy in law and human rights, especially relating to gender and children. She regularly conducts training programs for the judiciary of Maharashtra on child rights and laws.

She has recently drafted the regional protocol on trafficking and commercial sexual exploitation of children in South Asia. She has been a consultant to international organizations, including UNICEF, Save the Children UK, Canada, and Sariq.

Bajpai has many publications to her credit, including a recent article on custody and guardianship in India in the Family Law Quarterly of the American Bar Association, as well as the very popular book titled Child Rights in India—Law, Policy and Practice, published by the Oxford University Press.

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