Even though our dictionaries, driven rightly by usage rather than some eternal unchanging meaning, see these terms as functionally synonymous, their original meanings were not so*. And not so for good reasons:
Bias is partiality, a tendency to favor or disfavor. Talk about the warp and woof of life!
Prejudice is pre-judgment, a deciding of a case prior to evidence or direct experience, a pre-conceived attitude.
And bigotry, a word of French origin (although the French say it is Grmanic!), is not a descriptor but a slur. It just means someone who is inconveniently attached to viewpoints that someone else thinks should change. It is in fact a biased word.So, for example, in the traditional meanings of these terms, the New York Times might accurately be described as "the newspaper of bias, prejudice and bigotry."
I am a bigot only in the eyes of those who dislike my opinions and wish to render them literally unthinkable and me morally out of bounds for polite society. So the word really is useless for anything but propaganda and name-calling. Merely a slur, it is the intellectual's version of poopyhead.
I am biased in favor of Italian food . Having experience of both that and, say, Hispanic food , no contest. I have investigated and made my choice. I am partial to one over the other. As I said, welcome to the warp and woof of life. It's just taste, sorta. I am also, though, partial to intelligent people over stupid people. Ah...now we are getting edgy. After all, don't stupid people have a right to be treated as if they were smart? Who are you to judge? Or suppose I were to express a preference for Italian culture over Hispanic culture. Or worse, Italian people over Hispanic people. This preference feels kinda, ya know, really kinda discriminatory. Suddenly we move from torta to tort.
Prejudice, although now almost universally condemned --again, only in regard to Approved Victim Groups--- is both a constant in the human psyche and not always a bad thing. Indeed, some would argue that it is a good and necessary thing and that the attempt to be utterly un-prejudiced is not only impossible but damaging. What after all, is parenting, but the instilling of pre-conceived knowledge, attitudes and behaviors into inexperienced little humans? Without it, you can't have a culture or even survive very long.
Having disposed of bigot, I would like to acknowledge and claim that I am both biased and prejudiced.
And I dare anyone with an IQ higher than their age to think that they are not.
In the end, of course, everything depends on whom and what you are biased and prejudiced about.
A lot of this lingo is merely the pieties and orthodoxies of liberal culture. Like most of liberalism, by taking a half-truth and raising it to the level of an ideology, it becomes a lie.
*Being a logophile, I can't resist the apocryphal story of Charles II's response on first entering Wren's new Cathedral of St Paul in London: "Awful! Pompous! Artificial!". In 17th century English, these words meant "Awesome! Majestic! Ingenious!" I believe am indebted to jpnill for this, from long ago.