If there is a difference, it is subtle and is more apparent in certain contexts.
A bias is something that is inherent in a person and tends to be negative. It is not usual that a person can rid themselves easily of bias - it is ingrained and the person may not be aware of it.
I would use unbiased in larger matters to indicate that you have not been affected by the rhetoric of any culture's or organisation's, etc., claim or influence.
I would use impartial when describing something you would say when there are two people you know who are discussing something, yet not agreeing, or one person is describing difficulties that he is having with another person or situation.
By saying that you will offer an impartial opinion, you are saying that you will stand aside from the emotions and personal advantages and disadvantages of either party and examine only the facts. A judge should be impartial.
A: "My brother wants to marry this woman - but she's horrible! I don't know how to persuade him that he is making a mistake."
B: "Let me give you some impartial advice - don't interfere."