"Wouldn't the collective bias of decision making bodies at any institution amount to institutional bias?"

Yes, but how are you thinking the former is demonstrated from the evidence? In most cases, I'd argue that institutional bias is strongly indicated by the policies adopted and enforced by an institution, as well as the justifications typically given for them. The issue is that when you look at the majority of universities, there's no real evidence of policies or justifications of policy that exclude conservative faculty or students, let alone for anything as deliberate as is implied in the "collective bias" of the decision makers at those institutions.

If we compare this claim with a real kind of bias that did exist in universities in the past - like women being actively discriminated against - I think we also see something important. In those days, women were fighting to get into colleges, weren't they? It wasn't that they were underrepresented because their values were persuading them away from higher education. The two are very different scenarios, and I don't know how you blame the institution or enforce fair and equal treatment when the institution itself comes to represent a value that some ideology rejects.

To me, that suggests a re-evaluation of the values espoused by that ideology might be more in order. Because even if we grant it for the sake of argument that the liberal environment at colleges makes many conservatives uncomfortable, why wouldn't the best solution be to push more conservative students and faculty to value higher education more and participate in it? Doing the opposite would seem to fit a narrative that's perhaps more palatable to conservatives that see themselves as independent and individualistic, but it's still extremely counter-productive.