Benazir is the daughter of Md. Abdus Salam and Kohinoor Salam. She began her dance career at the dance school of Abdul Hasib Panna called Nikkon Shilpi Goshthi in 1983 in Rajshahi, Bangladesh. She was considered the national child of the years 1986, 1988 and 1989 through a competition organized by the Shishu Academy of Bangladesh. In those competitions she performed Kathak, Bharatanatyam, modern dance and folk dance. She was awarded gold medals in Manipuri dance, Modern Dance and Katthak Dance in Dhaka Junior Art and Music Festival 1988, sponsored by British Council and ANZ Grindlays Bank. She won the first Prize in Classical Dance (Katthak) in the National Education Week, Dhaka, Bangladesh in 1990. She also won UNESCO Clubs Cultural Award, Bangladesh in the same year.
She received a scholarship from the Indian Council for Cultural Relations for her undergraduate (honors) degree in Odissi from Rabindra Bharati University between 1996 and 1999.