Had to do a bit of digging.
It seems there are 'permanent' analysers set up in 6 locations in the city. All of the permanent analysers measure Nitrogen Dioxide(NO2).
Additionally, there are mobile 'Passive Diffusion Tube' detectors which collect NO2 data for a month at a time. The quantity of these or frequency of their use in Edinburgh is not listed anywhere that I can find.
Particulates(PM10) are measured at about half of the permanent analysing stations (including Queen St). However mobile PDT detectors do not measure PM10.
2012 report here
Particulate exposure is known to be highly localised, and the above report does recognise that. As far as cyclists are concerned, diesel engines are the killers, whether bus or car.
I'd like to see greater efforts made to measure PM10 at times and places where it's having the greatest effect on the largest number of people, such as rush hour on Princes St with all the buses. We assume that this is being carefully monitored, but the evidence is that PM10 at well-known blackspots simply isn't being measured.