This citation describes Bertram as defender of Dover castle at the Battle of Hastings.
"Bertram de Esburnham, son of Anchitel, son of Piers, Lord of Esburnham, was Sheriff of the counties of Surry, Sussex, and Kent, and Constable of Dover Castle, in the reign of King Harold, which castle he defended against William the Conqueror, wherefore William, on his accession to the crown of England, caused his head to be struck off, together with the heads of his sons Phillip and Michael de Esburnham. Francis Thyn, Esq. in 1586, collected a catalogue of the Lord-wardens of the Cinque Ports, and Constables of Dover Castle, from the time of William the Conqueror; and makes this mention of the ancestor of this family: "Bertram Ashburnham, a Baron of Kent. was Constable of Dover Castle in the year of Christ 1066, being (as is said) the first and last year of King Harold; which Bertram was beheaded by Wil∣liam the Conqueror, after he had obtained the crown, because he did so valiantly de∣fend the same against the Duke of Normandy."
http://quod.lib.umich.edu/e/ecco/004868667.0001.000/1:10.12?rgn=div...