The Evaluation of measurement data - Guide to the Expression of Uncertainty in Measurement (GUM) provides the framework for evaluating measurement uncertainty. The preferred GUM approach for addressing bias assumes that all systematic errors are identified and corrected at an early stage in the measurement process. We review some procedures for treating uncorrected bias and its inclusion into an overall uncertainty statement. When bias and its uncertainty are recognised as metrological states independent of scatter in the test results, the uncertainty of the reference and uncertainty of the bias can be equated. The net standard uncertainty of a test result is the root-sum-square of the standard uncertainty of the bias and the standard uncertainty of measurements on the test. Since an incomplete and therefore potentially erroneous formula is often used for estimating bias standard uncertainty, we propose an alternative calculation. We next propose a graphical method using a simple algorithm that quantifies the discrepancy between the results of a test measurement and the corresponding reference value, in terms of the percentage overlap of two probability density functions. We propose that bias should be corrected wherever possible and we illustrate this approach using the graphical method. Even though this review is focused principally on analytical chemistry and medical laboratory applications, much of the discussion is applicable to all areas of metrology.