While an androgynous person retains the same gender-typed behaviour across situations, the bigendered person consciously or unconsciously changes their gender-role behaviour from primarily masculine to primarily feminine, or vice versa.
It is worth noting that this concept emerged from within the transgender community itself, rather than being adopted after it was created by another sub-culture (for example, transsexual was defined first by the mental health community).
Because bigender is still a self-applied label, it is not possible to give a definitive outline of the typical bigendered person. Any description of a bigendered person is just an example of what someone who identifies as bigender might be like. Although there are patterns, the only firm characteristic is the sense of dual gender. From the Wiki link Zenda gave
After reading the above bit carefully, I think there is a little bit of "I don't want to be called androgyne so I will make a new name and call it bigender". I dont agree with the simplistic definition of androgyne as its listed above either.