By "biased" you presumably mean that there is some non-linear structure left in the residuals. It's by no means obvious to me that this is the case here.
Before leaping to any conclusions - and certainly before losing any information by transforming variables into a less-informative state - I would look at more residual plots. An obvious one would be to give a different colour or shape to the residuals where the suspect variable has a value of zero and see how this impacts on the residuals.
