Does the word "pin" used in this context has the same meaning as "bias"?
Good guess! Actually, the expression "to pin someone down as [x]" in this context means to define or identify someone as being a certain way. Thus, the speaker says that although it's easy to "pin [down]" Nagini as evil, the character was made much more unexpected and nuanced than that. Ex: It's easy to pin down someone as good or bad from first appearances. Ex: He pinned her down as an interesting character.