"The hourglass and skull with a bone in its grim maw in the corner of the painting is an alchemical image of the triumph of the hermetic arts over death. Like many other musicians and music theorists of the period, including his fellow Oxford student Robert Fludd, Bull seems to have believed that music shared fundamental secrets with alchemy. It is not unlikely that the brilliant keyboard player was also an alchemical practitioner."
I assume the attached article is by him. His attribution of esoteric interests to Bull seems to be based entirely on his interpretation of the symbols in the portrait:
"A fine portrait of Bull (fig.1) hangs in the library of the Faculty of Music at Oxford. It was painted in 1589 and bears the inscription 'anno aetatis suae, 27'. In one corner of the picture are a skull and crossbones and an hourglass. These are not symbols of mortality but the alchemist's symbols of victory of life over death: Bull may have been interested in the hermetic sciences (as were others with whom he came into contact, including Hunnis and the Elector Palatine)."