Son of Willem Bentinck and Charlotte Sophie von Aldenburg. Married (1760) to Maria Catharina van Tuyll van Serooskerken, daughter of Jan Maximiliaan van Tuyll van Serooskerken and Baroness Ursulina van Reede (1719-1747). The couple had at least two children, Willem Gustaaf Frederik Bentinck (1762-1835) and John Charles Bentinck (1763-1833).
Boswell supped at Count Bentinck's on May 5, 1764. Boswell in Holland identifies the count as CFA Bentinck. Boswell had apparently met him sometime earlier, and possibly even on April 28 at Willem Bentinck.1 The count had a copy of Boswell and Erskine's Letters between the Hon. Andrew Erskine and James Boswell Esq. in his library. They dined together a few days later, and on June 6, shortly before leaving Utrecht, Boswell received a few letters of recommendation from the Count for his tour of the German courts.
Bentinck later served as an intermediary in the correspondence between Boswell and Belle de Zuylen.