One answer is grammatical. Bias is a noun, a category that includes every person you can know or every place that you can go or any thing that you can show. Biased is an adjective, which describes a noun.
Another answer is that there is no difference. When people use the wrong part of speech (as in That article about the new Taylor Swift album is bias), It’s easy to write the mistake off as laziness, or careless typing. But as Arika Okrent writes at Mental Floss, depending on where in the country you come from, “ed” might be almost silent. If you’ve only ever experienced the word through speech and you’re typing like you talk, you might very well write “bias.” Give it a few more years, Okrent argues, and “biased” might go the way of skimmed milk.
The most important difference between bias and biased (or, in a few years, perhaps bias and bias) is tonal. Biased is an accusation hurled at people or institutions, a shorthand for deliberately hiding or bending the truth, or even flat-out lying. It’s often reserved for people or groups we dislike. That reporter is biased. That whole news station is biased. Twitter is biased. In each case, there’s usually an implied against us.
In its adjectival form, biased is made to sound like a character flaw, despite the fact that all humans are biased. The problem with biased isn’t just that it’s mean, it’s that it’s a lousy adjective. Saying “that person’s biased” is the same as saying “that person’s a person.”
Of course, some biases are more dangerous and insidious than others, which is why it helps to have another term. In its noun form, bias feels a touch removed from its human creators, which makes it a much better term to use when we’re seeking out the invisible assumptions in our day-to-day lives.
Let’s look at what I hope will be only-somewhat-controversial example. Let’s say I asked you to evaluate two articles about pacifiers. One is posted on Fox News’ website and the other is posted on an NPR blog. If I asked you which article was more biased, you’d probably offer me some conclusions about where the article was published before you even got to the content of the article.
What if, however, I asked you not to look for which article was biased, but at what bias the articles showed? I could make the job a little easier by removing the news organizations’ names and just giving you two titles:
Article 1: “How to get the pacifier away from your two-year-old.”
Article 2: “Does your baby need a pacifier?”
Article 1 implicitly favors pacifier use to begin with (because you wouldn’t have to stop using pacifiers if you never started). Embedded in that article is an assumption that pacifiers were useful or valuable to begin with (or at least that whomever gave the pacifier to the baby in the first place thought so). Article 2 might not share that assumption about pacifier use.
It's not that either of these assumptions are wrong--there are enthusiastic supporters of both positions and no kids seem the worse for having or not having them. The point is, the very questions writers ask can be evidence of bias.