"Battening down the hatches" was the practice aboard old-time sailing ships when bad weather was expected.

Hatches are large openings in the deck through which cargo and stores are loaded aboard. On wooden ships, the hatch covers were planks, which are not watertight. So the planks were covered with oiled canvas, and to prevent the canvas coming off in the gale, long wooden strips (battens) were placed over it and nailed down.

Of course, once the hatches were battened down like this, you couldn't use the hatchway, which is why this was only done when extreme safety precautions were considered necessary.

Modern steel ships have waterproof steel hatch covers, so battening down is not necessary. I have no idea whether Bounty had large hatches requiring battening or not. Probably not, since I'm sure modern technology would have provided it with waterproof covers anyway. Which may be why, in the aerial photos, the hull still seems to be semi-afloat, if waterlogged.