"Errol reassured the woman, advised her on her breathing and helped her bring her new child into the world. He then held the baby safely till the ambulance arrived," the Commissioner said in his regular blog.
"This was a highly stressful incident that posed a very real risk of harm to mother and child. Errol's ability to step up and take control is a great example of the skill and professionalism of our staff under pressure."
Mr Bush congratulated the new mum and Mr Diprose.
"One of the great things about a career in policing is the huge variety of tasks we're called upon to perform - often completely out of the blue," he said.
"And one of the great things about our staff is their ability to rise to any occasion, no matter how unexpected."