Bancroft grew up in Lakewood, California, from a working-class background, where his father was a housepainter and his mother worked at a grocery.
He attended the California Institute for the Arts (CalArts), where his academic studies focused on trumpet and his mentors included Edward Carroll.
[1] One of Bancroft's earliest experiences in conducting was the direction of an ad hoc ensemble in the Requiem of Wolfgang Amadeus Mozart, in a memorial concert for his father in 2010.
[2] In The Netherlands, he participated in the Nationale Master Orkestdirectie via the Amsterdam Conservatory and the Royal Conservatoire of The Hague.
[4] In September 2019, the BBC NOW announced the appointment of Bancroft as its next principal conductor, effective with the 2020–2021 season, with an initial contract of 3 years.