I just want to add that a lot of work goes into predictions of abundance, for objects including those we have not detected so far. There is some similarity to exoplanets - where we know that a method has a detection bias. If you can quantify the detection bias perfectly, then you can get the total abundance for different sizes.
One source gives a pretty good idea. Many references employ the D^-2.3 relationship, but it can occur as D^-1.3 as a cumulative metric. It's interesting that smaller sizes have been found to follow a different pattern. I strongly doubt that this pattern would continue to extremely small sizes, below D=0.1 km. As a mathematical statement, integrating to zero diverges.
I built some numbers for coefficients of the above relations with simple Excel calculations. To give you an idea of how the count changes with size, I took two regions of the above pdf. The region from 6 km to 1000 km contains on the order of 90,000 objects. But you're also interested in small bodies, so I also integrated the D^-4 relationship from 0.1 km to 6 km. That gives about 15,000,000,000 objects (15 billion).
If you decreased the lower bound from 0.1 km to something smaller, the count would be even more (likely by orders of magnitude). But we have no idea what relationship should hold there. Notice that the error bars grow as you go smaller? We don't have a good idea what the prevalence of small and microscopic bodies should be. Go small enough and you're at molecular sizes, so you could get a measure of the particle density in the solar system. But at that point, completely different factors are driving it (like atmospheric escape and solar wind), as opposed to the gravitational collection and breakup of bodies, which is what we think of as asteroids. We can put some bounds on the numbers - because space probes apparently didn't get smashed by micrometeorites. Regolith studies could also give some indication.
To get particle density, take the number you like for number of objects and divide by some rough metric of the volume that defines the asteroid belt. The uncertainty from that will probably be less than the count itself so I wouldn't worry too much about accuracy.