Born in Tollygunge, Kolkata, India, Shome grew up all over India since her father was with the Indian Air Force. She went to Delhi's Lady Shri Ram College and became a part of Arvind Gaur's Asmita theatre group. She moved to New York in the Autumn of 2004 for a master's programme in educational theatre at New York University, where she remained until visiting Mumbai on holiday in February 2008. Thereafter, she took up residence in Mumbai and, after completing some outstanding projects in New York, she returned to India in May 2008. In New York, she also taught theatre to third degree murder convicts at a high security US prison.

She played Alice in Mira Nair's feature film, Monsoon Wedding, and played Deepa in Shadows of Time (Schatten der Zeit), directed by Florian Gallenberger. She played a nun in the Australian film, The Waiting City by Claire McCarthy. Italo Spinelli's Gangor, based on Mahashweta Devi's novel had her playing a social worker. She also worked in Qaushiq Mukherjee's Tasher Desh. She played Mrs. Ahmadi in the Hindi political thriller film Shanghai directed by Dibakar Banerjee. About her performance in Shanghai Rediff wrote "Shome created one of this year's most heartbreaking performances in a Hindi film".^[7]

Her other roles have included Lara in Little Box of Sweets (directed by Meneka Das),^[8] Jaya in Long After (short film, directed by Afia Nathaniel) and Miraal in Butterfly (directed by Tanuj Chopra).

Her performance as a girl who is raised as a boy in Qissa won her the best actress title in the New Horizons Competition of the seventh Abu Dhabi Film Festival (ADFF). She shared the title with Norwegian actress Julia Wildschutt.^[9] She would be next seen in the film Children of War, which based upon Bangladesh Liberation War of 1971.^[10]