Bajpai did her schooling in St Louis Convent High School in Mumbai followed by Bachelor of Commerce from Jaipur University. She is trained in street jazz, Bharata Natyam and a few other dance forms. She also did theater for a year and a half and appeared in advertisements before making her TV show debut. Bajpai made her first appearance in the 2011 Bollywood film My Friend Pinto playing a small but noticeable role. She then made her small screen debut playing the character Krissane D'souza in the MTV show Warrior High. She is also the main lead in the upcoming show Hip Hip Hurray. Bajpai plays a super rich girl, Tasha, whose parents are separated.