If Ditto transforms into Greninja with Battle Bond, it copies the Greninja's current form (either standard or Ash), to include the ability slot, but that ability cannot be functional for Ditto. If it copies standard form and then gets a KO, it cannot change forms from there.
The note about "can't copy Battle Bond" refers to moves like Entrainment and Role Play. Battle Bond is one of a class of form-changing abilities, along with Zen Mode, Stance Change, Disguise, and so on. Form-changing abilities are considered essential to that Pokemon's function, so the game gives them special deference by making it impossible to overwrite those abilities with something else, and just as impossible for other Pokemon to use those abilities for themselves.