Born in 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 murder convicts at a high security US prison.