Personally, I will say that the notion of news "offending" due to editorial stance strikes me as an awful attitude to have. I am only "offended" by poorly thought out, sensationalist, over-emotional reporting that is devoid of facts and plays on fears (this type of "reporting" occurs on both sides, unfortunately). I may
disagree with a well thought out opinion, but a well thought out
opinion being actually
offensive? What an awful thing to think!
At any rate, even back in the old days of media there certainly were many choices for conservative news. Jim Lehrer's PBS Newshour on TV, many regional newspapers, and business papers for instance. Populism had a few non-gossip national tabloids like the New York Post; talk radio too.
It is true that a lot of media was dominated by a modest-left stance (talk radio being the exception), but I don't find bias a problem per se (we all are biased after all). I lean modest liberal personally, but back when I actually watched TV news I thought the PBS Newshour was the best of the lot, as it seemed to avoid some of the scare story traps the "big three" occasionally worked themselves up over.
Of course, these days, thanks to the web, you have every opportunity to silo yourself in one bias you are not "offended by" if you want.