One of the most effective ways in my opinion this is achieved and addressed and by far the most common one in my academic context is rather simple: method.

A clearly defined method/approach to whatever your research question is based on a theory will heavily reduce any bias that might be present, cultural, personal or otherwise. Clearly spelling out that you are e.g. conducting an analysis based on discourse analysis, why this is the best approach to your question, and what the underlying theory gives you in terms of tools and understanding not only structures your work and gives you a framework in which evidence is interpreted but also minimizes any bias you might have.

Of course, your question and choice of method are influenced by where you come from and which you university you have been taught at / what you read previously. Someone who is a staunch anti-Marxist is less likely to employ Gramscian theory as a method for interpreting history. Of course, there can be debates about how useful it is to approach a certain question with one specific set of method and theory but since they are open to scrutiny to everyone who reads your methodological chapter, this issues remains within a scientific frame.

Similarly, your research question will be influenced by where you come from and which languages you speak e.g. and other similar factors. But while there still can be a debate about asking the right question, it is generally totally ok that people from different contexts will ask different questions – otherwise we'd end up writing the same and that's after all, not really the point of the whole exercise.

Interesting question! I was actually having a conversation about this just last night.

So when I think of a bias, I think of a pattern of behavior. A person with a bias favors or disfavors a thing, person/people, idea, whatever. So when whatever that thing they have bias towards comes up, they demonstrate a pattern of following it.

When I think of those biases you mention based on culture and environment, I think more of a point of view. Points of view could easily become a bias, but the idea is that we can keep out point of view in check before we form a rigid pattern of behavior. One key way of doing this is getting other people involved. The more points of view you have, the more you're able to eliminate unfair biases and reach a point of verifiable "objectivity."

Here is an example of what I'm saying. If we look that picture, a person's bias is dictating what research they're studying and conducting. Thus, their conclusion is based on that bias.

If we look at this picture that involves multiple viewpoints, we can start to see how a bias can be eliminated. Bringing in opposing viewpoints, similar viewpoints, and neutral viewpoints will balance out any biases we cannot filter through a personal reflection. The goal is that by the end of their study/research, they have a more objective viewpoint.

There are other ways we can go about avoiding, balancing, or eliminating those biases, but this is one big way that I utilize.

History isn't a "science." Objectivity is a value, but it is not truly achievable. The way we tend to tackle this is to look at things as neutrally as one can, and to occasionally "check oneself," but ultimately one is also engaging with other human beings with different backgrounds and they are all-too-keen to point out where they think their peers are going wrong. One tries to be aware of one's biases, but one should not confuse this with expunging subjectivity. I read the past in certain ways because of my subjectivity, and that gives me unique interpretive perspective. The embrace of subjectivity, while hewing to norms of intellectual honesty and good practice (citation, etc.), is what gets one a nuance historical narrative and argument that also accounts for evidence and empiricism. Historically, in many fields of research, attempting to radically expunge bias, subjectivity, and the like, often leads towards a masking of it (with, say, numbers), whereas admitting subjectivity necessarily exists and taking care to be self-aware (and self-admitting) about its role in the creation of the work leads to more honest, less self-deceptive output. When I write, I try to be very clear where subjective interpretation is guiding my approaches and arguments — I find, personally, that it actually strengthens my case, rather than weakening it.

To add another wrinkle to all of this, a proper historian is also aware of the fact that the norms of objectivity are themselves historically determined along with everything else! Objectivity in science has changed forms several times, and the debate about the capabilities of historians to be objective has engendered considerable discussion in the profession. On objectivity's checkered history as a scientific virtue, see Peter Galison and Lorraine Daston, Objectivity (MIT Press, 2007). For a nice discussion about how this question has been batted around by American historians, Peter Novick's That Noble Dream: The 'Objectivity Question' and the American Historical Profession (Cambridge University Press, 1988), is a very nice probing of these debates, and is (in my opinion) required reading for anyone interested in the study of history.

To throw out an example of a scholar tackling this question, Brad Gregory has written an interesting article about religious/confessional biases by religious scholars (especially of Reformation historians). His thesis - certainly not uniformly accepted, and probably grossly simplified here - is that religious scholars writing from a secular or atheistic viewpoint are as fundamentally biased (on metaphysical grounds) as historians who are practicing Lutherans or Catholics. While these biases don't invalidate the work, he certainly argues for scholars to be more cognizant of them as they do research.