Does a reference to a work inside a footnote have to be in the bibliography? If in a footnote I write something like, "For more on the debate, see... so and so" 

Does that work I referenced in the footnote go on the bibliography page even if I did not reference this work directly in the essay?
You did reference it, it is in the document, so of course it goes into the bibliography.

Imagine the other way round: Someone reads the text, finds it interesting, sees that there is more to be found about this topic in a source and then can't find said source...