There are at least two acts called Bombay:

1) A three piece indie rock act formed in Amsterdam, The Netherlands. Originally known as Bombay Show Pig, the lineup consists of Mathias Janmaat on vocals and guitar, Lisa Ann Jonker on vocals, drums and keyboards, and Gijs Loots on bass. The band announced their split at the end of 2016.

2) A four piece punk band from Plymouth, Massachusetts. They released a three song EP called "Writer's Block" in early 2011 on CD and cassette tape. Their second EP, You Should Worry, was released in May, 2012. In February 2013, they released two demo songs recorded in 2011 by the name of AI Demos.
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