is traditional news media "liberal"? I think you can make a case for yes and no. I lean "No" (I think the term "liberal bias" is construct of conservative epistemology and ontology) but I have a counterintuitive reason why you could answer this question "yes"

How would society look if the dominant institutions of the free press and education were conservative?

I feel like you could make a case that news and pedagogical cultures need to bend liberal (lowercase "l" and not to be mistaken as synonym for support for progressive ideas & Democratic Party) to function.

If they were conservative, their function would be (I'd argue, overwhelmingly) indoctrination.