I'm just naturally unbiased, so thankfully, it's not something that I need to worry about :P
The "Bias Adjusted" score is an peculiar feature. I actually find it pretty interesting, though I'm sure in practice any impression of objectivity it provides is wholly illusory. It seems like a fun quirk that helps that particular site stand out, at the very least.
The latter is probably the only thing that really matters when it comes to scores, anyway. After all, what are they for, if not for being fun to analyze and argue about? I've never found that a review's core really helped to improve my understanding of a game beyond what text can do.
I agree with others who suggest being up front with ones biases, with the caveat that I try to do a lot of consideration of my own biases before I set out to review a game. They're not always legitimate...sometimes putting them down on paper shows them to be shallow or poorly-conceived, and you can work through them. On some level, the biases will always be there - best to acknowledge your feelings and make doubly sure that your audience is on the same page. They might get huffy if they don't like your opinion, but it's better to give 'em all the information to work with than to leave them with half of the story.