I doubt you can prove ‘bias’ in a media outlet as if some kind of hard science question. One of the ‘studies’ I recall about Fox News viewers being ‘misinformed’ (which as has been noted is not really the same as proving the outlet they watch is ‘biased’, anyway) had a question asking people, a couple of years ago, after 2009, whether the US was in a recession. Those who said ‘yes’ were classed ‘misinformed’, since the National Bureau of Economics Research had declared the ‘crash’ related recession as over in June 2009. Please. Very few people answering such a question either way will actually know the NBER’s end date for the recession, and it wasn’t what they were asked. I knew the date but would have answered ‘yes, still recession’, because in the colloquial meaning of the term it still was (and is), the economy sucks, a common sense fact IMO (though reasonable people can disagree the extent partisan differences in policy account for that). People more critical of the current administration are more likely to see it that way, and more likely to watch Fox
Filter out the ‘studies’ which are effectively push polls like that one was, factor in other studies finding for example that Limbaugh’s audience considerably outperformed the general public on a list of strictly factual civics questions (who is the House minority leader, that kind of stuff) then come back with the ‘proof’ which audience is ‘less informed’. 99% likely, a muddle. And don’t forget the big picture back drop. When all the news and punditry has been disseminated and people go to the polls, it’s obviously the Democrats who rely more at the end of the day on poorly educated and informed voters. That’s the system, one person, one vote. But there’s a serious glass house problem when the left gets too wound up about ‘uninformed’ people on the right.
On ‘bias’, I understand that people pretty far to the left don’t view CBS/NBC/ABC/CNN as liberally biased. Those stations’ coverage proceeds on assumptions that real leftist might view as ‘rightist’, ‘corporatist’, ‘too US centric’, etc. But that’s subjective. If you’re further to the right, their operating assumptions appear more liberal. But OTOH here’s AFAIK an undisputed fact: the great majority of reporters and editors from those outlets personally vote Democrat. Again to a real lefty, voting Democrat doesn’t make you a ‘progressive’. But to a Republican, having the news filtered and interpreted for you almost strictly by Democrats could be perceived as a problem, is that so unreasonable?
And that’s where Fox comes from, basically, decades of having the news fed to us (all, left and right) almost exclusively by Democrats working for the ‘prestige media’. That was the business opportunity Ailes identified (which is what it was first and foremost). So indeed Fox is very self conscious in presenting things differently than the traditional ‘almost Democrat voter news people, but trying to be fair’ approach, different style and feel as much as anything else (when did Today etc ever invite on country singers or NASCAR drivers before Fox either? that’s part of it also, different cultural wavelength not just politics per se). And Fox also presents a lot of commentary programming, but not only ‘so do the others’ but the others have followed that model, to a degree, because of the success of Fox. MSNBC, its (few) fans pop a vein hearing it but it’s true, is a mirror image imitation of Fox more than anything else, it’s just not as commercially successful. And CNN has long danced around with various formula’s which are based on targeting Fox infotainment shows (Piers Morgan’s snivelling Limey style liberalism, other personalities sticking with the old ‘I’m a Democrat but I’m being fair’ formula to various degrees, etc). CBS/NBC/ABC OTOH have all kinds of (complete schlock) ‘pure entertainment’ shows to air most of the day, so aren’t really in the same business as CNN, Fox News and MSNBC.