It seems to me you're using "bias" in an unusual way, so it's probably worth talking some more about what you mean by it. I'm going to try and explore some of these meanings and leave the substantive argument about the question itself to people who know more about historiography.

Here's a definition of "bias," from dictionary.com:

a particular tendency, trend, inclination, feeling, or opinion, especially one that is preconceived or unreasoned

So an author who is sympathetic to the Nazis might play down the atrocities they committed. They might make arguments as to why they weren't so bad, interpret sources spuriously, or concentrate on looking for evidence supporting the Nazis.

Probably a more common example is a nationalistic bias. People are proud of and want to be proud of their country, so they portray it in a positive light - and its enemies in a negative one. You can see this happening on both sides of the historiography about the British Empire.

Bias can be very subtle, extending to our fundamental assumptions or the topics we choose to look at. For example, most countries school history textbooks concentrate on that country. There are decent reasons for that, but it is likely to give an exaggerated view of the country's importance. Reducing bias is generally considered an aim by historians, but everyone suffers from it to a degree.

The way you're using "bias" seems to be more like "judgement." In both common senses of the word - concluding that something is true and making arguments for it - and making normative judgements - that things are right or wrong.

The former is essential in history. There's no such thing as simply presenting the facts. Choosing a fact to present means making a judgement that it is important. Then you are deciding how it fits in to a framework of other facts, trying to draw causal relationships between them, etc.. Actually, even before that, there is probably some interpretation of source material or evidence - "is this document true?"

Historical writing will also be underpinned by theories about how history works and what matters. That could be, for example, the "great men" approach, where history is driven by a few outstanding men (very unfashionable currently). It could be "longue durée" where geography and physical factors shape history over centuries. Or any number of possible approaches. All of these approaches have strengths and weaknesses, things they ignore and things they highlight. A historian has to make a judgement on which theory to use.

Linked to this, you might find this thread talking about "truth" interesting.

Lastly, is moral judgement a task of the historian? This is probably the most contentious. Is it the role of a historian to say that the holocaust was bad? To argue whether the Korean War was right? Or if the British Empire was good or bad? To make judgements about Napoleon's moral decisions? I think most historians would say this is not their role, but it's a tricky question.

(edit: added in the link.)

The quote I like to use when this question comes up: "objectivity is not neutrality." One can be objective, but not neutral. Which is to say, one can objectively come to a conclusion about facts that is quite strong. This is not bias.

Bias in this framework is when a lack of neutrality interferes with attempts at objectivity. It is when the cart starts to lead the horse — the conclusions dictate the research, not the research dictating the conclusions.

Obviously in practice, these things are complex. History is not a science. One has reasons for pursuing certain lines of thoughts, privileging certain kinds of evidence, that people who disagree with one might call "bias" and what someone more charitable might call "judgment." The line between bias and this kind of thing is an acknowledged fuzzy one.

The usual caveats about the impossibility of achieving true objectivity apply (the idea is best as an ideal relating to intellectual honesty, not something that denies the role of the historian as a subjective individual working in their own time and context).