I guess the simplest relationship between them I can think of is that BIAS is something that may be determined as a part of the calibration process.
Sounds like from your latest posting that it is the difference between the "bias calculation process" versus the "calibration process" that is in question.
There are two uses of the term calibration:
a. Verification that a measuring instrument is still measuring within its specified tolerances, or if not, documenting/adjusting as needed to bring it back within specified tolerances. This implies doing so with measurement standards of know accuracy (traceable to national or international standards). This also implies a certification process that the instrument may be expected to remain within tolerance for a given period of time and to a given percent confidence.
b. The adjustment process on a measuring instrument to optimize its measurement accuracy.
(I tend toward (a) above).
The "Bias Calculation Process" is a little different in that it is a subset of (a) above (I am not an expert in this specific term, so I am commenting based on my background in calibration), and does not necessarily apply only to measuring instruments.
The "Bias Calculation Process" is specifically determining the amount of error between a unit under test and nominal. The unit under test may be a product. If you manufacture a screw with a given thread pitch, you may sample units from the production line, and measure their actual thread pitch in comparison with a calibrated thread pitch "master" (or other source of determining nominal). This would be a bias calculation, but not a calibration. The nominal may be a thread master. This thread master may be sent out to an accredited calibration lab and certified to a given value and a given uncertainty (this is a calibration). Then the calibrated thread master is used to determine bias of the product (not a calibration).
Calibration refers more to certification that an instrument or gauge meets specified tolerances.
I hope the above helps clarify this for you.