First, based on customer requirements, you should set specification limits (Lower specification limit and Upper specification limit) for measurement mistakes. Based on that you have to show that bias is in specification limits by doing MSA (Measurement system analysis).
Based on Six Sigma methodology for an instrument, we have Machine bias, that is the case when different instrument gets detectably different averages for the same measurements on the same parts.
For the stability, you should compare the measurements at one point of time to measurements taken at another point in time. If there is consistency across time than it is stable.
Linearity exists when accuracy is consistent across the entire range of possible values. So you can draw a diagram with at least 30 measures to see is linearity achieved.