With only two exceptions bias in the public sphere among conservatives is motivated by ideology. Those exceptions are economic probity and the aesthetics of consensus. In other words, a conservative might without ideological input take a certain line on an issue if it is lower-cost or if it conforms to the feelings of the majority. All other justifications for conservatives are based purely on ideological considerations.
On the Left, on the other hand, bias is exclusively predicated on reason. A progressive will tend to favour a particular line of thought because it is rational in light of advances in ethical and moral etiology since WWII: human rights, the conservation of the natural world, inclusiveness, tolerance and such. Once you accept that the modern social compact has virtues by reason of one or more of these considerations, it is rational to take it the next step down the track toward the perfection that etiology implies. To wish to halt progress is to flirt with the aesthetics of consensus, and to swing into the camp of the conservatives, which is something that progressives abhor in general. However there are many flavours of progressive just as a conservative might take a progressive line on one particular issue while remaining wedded to the status quo with regard to others.
The notion of bias has, furthermore, an undeservedly bad name. Popular censure of bias is particularly prevalent in discussions of the media which, sitting between the major actors in the public sphere and the public itself, is assumed to require a perfect surface that does not distort messages in a perceptible way. Avoiding perceptions of bias is a major concern of all media outlets regardless of how openly they pursue their overt agenda. However it is a myth, and one that we are best to be jack of, where we should prefer fairness. Fairness assumes that the person doing the reporting is a person - which, in all cases, they are; dogs do not report stories in the media, for example - and also assumes that bias is implicit in the notion of personhood; we all have personal views on a wide range of public issues.
In lawn bowls the game would be unthinkable without bias on the balls used to play it. In the public sphere we should also take for granted that bias exists, but that the reporter whose work we are reading has striven to be fair to all parties in the case.