You are not alone. I went to a music school majoring violin for eight years. Not quite the same as having a BMus in US, but a long way in the same direction.

Music is never a background to me. I will occasionally switch music on while working, but with the specific purpose to switch my mind. Usually either when I am trying to work out the best solution to some problem and I need to get away from it for a second or when I am task switching.