His unconventional career structure has taken him from a medical degree to being a jazz musician and composer, and more recently running both a record label, Caber Music, and an educational company, Caber Enterprises, with his twin brother, Phil. An invitation to sit on the assessment panel for the SAC awards helped Mr Bancroft to decide to act on his growing frustration with his career path and apply for one instead.
The awards, worth pound;30,000 each, are offered annually to proven individual artists who live and work in Scotland for projects which aim to explore creativity, develop new work - which must be shown to the public on completion - or engage in imaginative collaborations.
"My work as a composer has gone on the back burner since the record label was launched five years ago," Mr Bancroft explains, "and my proposal is to do some new work for a large jazz ensemble, to revisit and record some of my older work and also to do some new work in schools as part of that process.
"It all came from the questions of who you are and what you are doing with your life.
"When I was in the fifth form at Edinburgh Academy, an actor named Victor Spinetti came and talked to us about life and how you decide what you do with yourself. He wasn't giving easy answers or prescribed paths, but I found it very powerful and inspiring."
Since Mr Bancroft's own path has taken him from a privileged education in Edinburgh and at Cambridge University, through major life and career changes, he felt that he could offer something similar as part of a music project for upper secondary pupils if he is successful in securing one of this year's Creative Scotland Awards.
"As well as playing music, I would talk to them about what they want to do, whether it is medicine or science or arts or business. It wouldn't be a matter of providing definitive answers, more a way of sharing my experiences and letting them engage with the kind of decisions and paths they might follow," he says.
"I'd like to take this into a wide range of schools and share my experience with kids from very different backgrounds. They might just think I'm a weirdo, as some of my class did when Victor Spinetti came, but some of them will get something from it."