This study from 2006 found detectable concentrations of cockroach allergen in 63% of American homes. If @marinelife‘s population estimate comes from this source, then it is actually a range estimate of 18,000 to 40,000 per apartment in poor areas.
I now know more about cockroaches than I ever wanted to. There are different populations in suburban homes compared to urban homes. They live all over the place: houses, other buildings, sewers, and in other outdoor places. I’m not going into their role in passing around diseases and as asthma allergens.
To answer this question, I need to know why you need the data. If this is just for fun, then make up a number. Anything will be believable because no one knows the relationship between the visible population and the hidden population. If you are working on a real health issue, then some of the studies on allergen prevalence will be more useful than population estimates.
If you want to make a serious population estimate, then do some research on insect biomass worldwide, and estimate the population in the US, adjusting for type of environment. You can triangulate that by using the various population estimates out there for urban and suburban and rural settings, multiplied by populations of those types of structures. You’d need to add an estimate for environmental population, as well.
So you’d do a top down and a bottom up estimate. See how close they are. Maybe take an average. But really all you have is a guess. So you might as well take a wild guess now and be done with it, unless, for some inexplicable reason, being accurate matters.