A bias cut fabric will stretch a bit and can give you a smoother piping. I try ( notice I did say try) to use only bias as it is a bit better result. Sometimes I just do not have the fabric to do a bias cut for piping.
There is a method that does not use cording for a false piping. You just fold the fabric in half and sew in so only 1/4 inch or so is showing. This method you do not need bias . I often do this as it give a vary similiar effect with out the step of the cord ( I never seem to have the right amount when I need it).