Bancroft studied trumpet at the California Institute of the Arts, alongside additional studies in harp, flute, cello, and Ghanaian music and dance. He then went on to receive an MMus in orchestral conducting from the Royal Conservatoire of Scotland. While studying in Scotland he played trumpet with the BBC Scottish Symphony Orchestra on many occasions. He continued his conducting studies in the Netherlands and is a graduate of the prestigious Nationale Master Orkestdirectie run jointly by the Conservatorium van Amsterdam and the Royal Conservatoire of The Hague. As a student, his main mentors were Edward Carroll, Kenneth Montgomery, Ed Spanjaard and Jac van Steen.