Wherefore it happened that one ship of the Templars, carried away by the violence of the current, was cast over near the side of the city toward the enemy, who for a longtime assailed it with barbots [footnote 62] and grappling irons, hurling out Greek fire and stones from the towers above; and since they could not prevail on account of the bravery of the defenders, they eagerly climbed up the ship, and throwing themselves headlong into it, descended upon the Templars. When they had fought there for a long time, the ship at last was pierced (whether by the enemy or by our own men we do not know) and sought the depths, drowning Egyptians with Christians, so that the top of the mast scarcely appeared above the water. And as Samson “killed many more at his death than he had killed before in his life" [Jgs 16:30], so also those martyrs dragged into the abyss of the waters along with themselves more than they could have killed with swords.
From Oliver of Paderborn "The Capture of Damietta" ca. 1217-1222 as translated in Crusade and Christendom: Annotated Documents in Translation at page 175.
See also Christian Society and the Crusades, 1198-1229: Sources in Translation at page 73.
An independent source, as quoted in The Knights Templar at page 199 states:
The Saracens boarded, until there were a good two thousand men there. The Templars were below decks, and seeing there was no escape, they resolved to destroy their enemies and die in the service of Our Lord. Therefore they took up hatchets and chopped through the hull of the ship. She went quickly to the bottom; one hundred and forty Christians drowned -and more ...
Similarly, in an article dated 4 July 1868 in Freemasons Magazine and Masonic Mirror vol. XIX (reprinting a section of the book The Knights Templars by Anthony Oneal Haye), at page 524, states:
one of their vessels was driven against the bank and boarded, upon which the Templars, with their axes, cut holes in her bottom, and both they and their enemies were drowned
So, it was not a "bombing".