It looks like the Admin bonus involves more factors than I originally thought.
So far factors that need to be taken into account are:

1)Gov's Management

2)Tax rate

3)Buildings (trader, farms, roads, ports all have an effect though it is rather small, probably mines too and temples which boost farming or trade should also be looked at)

4)Population (yes, an increase in population gives an increase in Admin bonus and what's more confusing is it may not be compounded by tax rate as the other factors - there is a significant disparity in ratios for different population sizes)

5)Campaign difficulty (appears to be an overall multiplier as for other income sources)

This will need some time to sort out (assuming there are no additional factors in play). Would be nice to have someone work on this and shift it to the Ludus Magna forum when we've some solid findings.