Just because one believes in something doesn't necessarily mean they are fully biased towards it. They can still be quite objective about their belief as well. I don't believe in the singular almighty god prevalent in the dominant religions (Christianity, Judaism, and Islam), but I'm by no means biased against such ideas (assuming the concepts are presented to me in a non-forceful way. Trying to shove one's beliefs on me is when I will push back.)

You can call me agnostic (I don't really commit myself to that term, though if needed, I would probably state that over atheist for now), though leaning toward Shintoism. (Shinto concepts make more sense compare to some of the western religious concepts.) However, I don't put my belief at the forefront of my mind and am very open to other ideas. Belief =/= bias.

Another example (if somehwat weaker) is how this site's upload approvals are manage. I can very well believe an image is fugly as hell and should be deleted. If I was truly biased to my belief, I'd delete it on the spot (assuming it met all the technical requirements for the site). However, I tend to leave my bias behind and leave such an image for review by other mods for a second opinion.

A bias or belief may lead to one or the other, but they don't really equate to each other, if you get what I mean.