Jay Bentley and the Jet Set are not identifiable as a recognized band or musical artist in the realm of music history. It is possible that there may be confusion with the name. Jay Bentley is known as the bassist for the influential punk rock band Bad Religion, but he has not been associated with a project titled "the Jet Set." Therefore, providing a detailed description of their musical style, significance, and history is not feasible. Please check the accuracy of the name.