Certainly some of us do.  We may happily endorse prejudiced views about certain groups, or reluctantly admit that we hold prejudices of which we're not proud.  But for many kinds of biases, research suggests that we're not very good at knowing we have them, or how strong they are.

Research shows that while levels of explicit prejudice (e.g., racism and sexism) have gone down, implicit prejudice - our unconscious associations between certain groups of people and negative attributes - is alive and well.  What's more, the two are often unrelated. What you think you think about African Americans may not match your automatic reactions or unconscious assocations.

According to the findings, implicit biases are quite common and robust (many people show larger differences in their implicit associations with elderly vs. young people, for example).  In addition, these biases are present even in people who honestly believe they have no bias or prejudice towards that group. Most importantly, these biases are not harmless.  Research shows that they predict subtle (and sometimes not-so-subtle) acts of discrimination, such as being less friendly or warm towards a person, or evaluating their work more harshly.

Of course not everybody has negative implicit associations about other ethnic groups.  But many do. And they don't know it.  So unless Sotomayor harbors explicit prejudices that she is willing to parade in front of the whole senate, we probably won't learn much about her biases by asking her.  And even if she does have implicit biases, there is no reason to think all the other justices don't as well.