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 referenced the work in your footnote. Your footnote is part of your essay. Therefore, you referenced the work in your essay.
But, really, I want to take issue with what seems to be the premise of your question. It seems to me that you're thinking in terms of rules: "I must include something in my bibliography if it meets condition X, Y or Z." This is the wrong way to think about almost every creative act, such as writing an essay.
Instead, consider why we have a bibliography at all. First, it's so that the reader can find full details of every source that you use, so that they can also refer to those sources. OK, so you could give the full details in your footnote. Using a bibliography also has the advantage that it means that somebody can see at a glance what your sources are, which doesn't work if some of your sources are in the bibliography and some are elsewhere. Also, a reader is likely to expect that all your sources will be in the bibliography, if there is one.
Also, consider what the reader will expect.
"Is it likely to help the reader?" is a good way to approach many writing questions.
In this case if the footnote is helpful then the bibliography entry is just as helpful. If the footnote isn't helpful it shouldn't exist. What would be unhelpful is effectively saying to your reader: "For more, see a piece of work I'm only going to hint at."