Grimwade records William Bowsey’s only mark, as a bucklemaker at 180 Bishopsgate, being entered in 1792. And no other information.
However research by Mike indicates that he was almost certainly the son of George Bowley [sic] an Oilman and Baker of London from 180 Bishopsgate Street who had him apprenticed to Jonathan Perkins I in 1785. William was made free of the Goldsmiths' in 1792.
Bowsey is thus probably a misreading of Bowley by Grimwade
James Bowley took as apprentices William Salkeld in 1798 (premium £100) and William Joseph Robinson in 1805 (premium an eye watering £200).
Both indentures show Bowley had become a salt merchant at Bishopsgate Street and that he signed up the young men to teach that trade rather than that of a goldsmith.