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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.

George and William Bowley were together assessed to Land Tax on 180 Bishopsgate Street until 1800 after which William was assessed on the property alone until 1805.
He appears to have married around 1800 as there was a christening of Susan Elizabeth, the daughter of William and Mary Bowley, registered at St Botolph, Bishopsgate in 1801. The register at St Leonard, Shoreditch shows a marriage in 1799 of William Bowley, but as a bachelor of that parish, to spinster Mary Hale of St Pancras parish. The record may be relevant.
He was listed in the 1802 Electoral Register at 180 Bishopsgate Street as having an entitlement to vote in respect of property in Elstree where he was listed as owner and occupier.The £100 from Salkeld in 1798 would have been useful in buying the property to house his wife and child.
The property at 180 Bishopsgate may have been sold around 1805 and the proceeds along with the £200 from Robinson used to purchase property in Half Moon Alley, Bishopsgate Street to be used as a continuing business address in the City. He was assessed to Land Tax on this property from 1806-16, a new tenant being named in 1817.

There is a record of William Bowley being born to George and Susanah on 6 November 1769 at St Ethelburga Parish, Bishops Gate, London that may apply.