A question I've pondered for a while is how does a historian keep their bias in check? For instance, I intend to become a historian primary studying Polish history. However, as a Pole and self-described patriot, I would be inclined to paint Poland in good light, and rivals of Poland (i.e. Russia) as villains. Thus, how would I keep my love for king and country outside of my writings in order to maintain objectivity? Is that even possible, or should I just study Classical Civilization instead (where I have much less bias)? Furthermore, is bias a problem in academic history?
It's not just possible, it is essential. Irish historians inhabit a similar cultural situation. My belief is that part of my patriotic duty is to give my fellow citizens the best, most accurate account of their past I can. It won't always make them happy but the alternative is to do something else and leave it to people who lack the training or inclination to even try to be objective.
OK, that's the why. How is the point of your training. The questions you ask and the subjects you study will be affected by your preferences but the answers should only come from the evidence. Second, kill your darlings; everyone has flaws so if you can't find any in your heroes, you're biased. Lastly embrace comparison, most patriotic biases treat their country as exceptional - the perfect nation or the perfect victim. Read about other countries and compare their experiences of religion, colonisation, state building, war etc.
Bias will always be a part of history but it is usually subtle. Most of it relates to genuine differences in how we see the world. For example the high unemployment can be seen as a sign that the government is incompetent or that it is implementing tough reforms. That debate is still going on over 1980s Britain. Good historians can overcome obvious biases but at some point you have to analyse using real values and beliefs. All you can do then is make sure you engage with alternatives. Also remember Keynes's great challenge "when the facts change, I change my mind. What do you do?"
Above all evidence, evidence, evidence!
All forms of writing, history being a prominent example, is biased in some way. If you give two historians the exact same sources and evidence, they could very well write a history with very different interpretations and conclusions based on the historians school of thought, background, political allegiances etc. Look at the Russian Revolution as a prominent example, conservative historians interpret texts by Lenin or Trotsky in very different ways than a Marxist historian would.
The best answer to your question would be to attach more emphasis on your sources than your personal beliefs, and most importantly to not let your personal beliefs pick and choose what sources you will use. This can be a trap for historians; although it isn't necessarily wrong to have a bias or a specific purpose when you write history, whatever you write will only be good history if you take into account a range of views and sources that might be the opposite of your own. Feel free to disagree with them, but you need to detail why and provide proper evidence to support your stance.
I do not believe it to be possible. We all have our biases and prejudices, and they show. It is natural and expected. But there are ways to write so that your work is better recieved. Something I do is give multiple points of view a chance, even if you are debunking them, it still gives that point of view a chance to be heard. Also, as another comment said, put your focus on the source, and not your bias. Use evidence to support your point of view. In the end, we are always encouraged to resource multiple sources, not just one, so even if one work is somewhat biased, there is another work with a completely different bias to offset it.