He is stated to have been the son of ‘a natural (born) Italian', who has been identified as Antonio Bruschetto, a merchant of Genoa who settled in Hackney, London, but of his early life nothing definite is known.
In 1594, he sought to be reappointed clerk of the Irish Privy Council, but failing to obtain that post he was granted the ‘clerkship of the casualties’ in the following year, and was High Sheriff of Wexford 1595–96.
He is stated to have been still alive in 1611, but probably died the following year, as his widow soon afterwards brought a lawsuit concerning trespass by a neighbour's cattle, which had strayed onto the Bryskett lands at Macmine and damaged the crops.
His chief original literary work was a translation from the Italian of Baptista Giraldo's philosophical treatise, which he entitled A Discourse of Civill Life, containing the Ethike Part of Morall Philosophie.
[1] Bryskett describes how a party of friends met at his cottage near Dublin in the late 1580s, among whom were Dr. John Longe, archbishop of Armagh, Captain Christopher Carleill (a stepson of Sir Francis Walsingham), Sir Thomas Norris, Captain Warham St Leger, and Mr. Edmund Spenser, ‘once your lordship's secretary.'
[1] In the course of conversation Bryskett says that he is envious of ‘the happiness of the Italians' who have popularised moral philosophy by translating and explaining Plato and Aristotle in their own language.
Addressing Spenser, Bryskett entreats the poet to turn his great knowledge of philosophy to such account, and as a beginning to give them a philosophical lecture on the spot.
Bryskett includes in the published work a few remarks made by Spenser in the course of the reading on various philosophical problems discussed in the book.
Bryskett upon the deathe of the most noble sir Philip Sydney, knight', and licensed to the printer, John Wolfe, on 22 August 1587.