 Busch was born in Bjerre, on Jutland, to a lawyer and his wife, and was the youngest of five children.His father hoped that he would follow him into the legal profession, but Carl was more interested in pursuing a career in music, learning to play the flute, violin, and cello.He studied and played under many of the notables of the day, including Niels Wilhelm Gade and Johan Peter Emilius Hartmann; he also worked under Johan Svendsen.