I too have wondered this for decades. However, I think it would be pretty hard to get a firm number as the number is relatively small compared to the population. If 25,000 individual people bicycle tour (any length of tour) in the USA in a given year, that would be only 0.00083% of the USA population, way to small for an accurate measurement I would guess.
Also, some questions pop to mind in trying to do the study. Do you include only citizens of that country (easier to survey but then not realistic), how would you define "cross country", i.e. east to west coast is pretty easy but what about NYC to Brownsville, TX? Then there is the proverbial what is a "tourer" (I DO NOT want to start a flamefest) question, i.e. ranges from must be totally self-contained and sleep out all the way to a fully supported credit card tour? Must it be totally self-propelled or can they take a bus/train/plane for a section of it (how big of a section)? Do they have to complete it or only INTEND to complete it but never did (got sick, in an accident, etc.)? How do contact them as some might miss the survey since they are out touring when the survey arrives?
I would think though that ACA would have a somewhat good base number based on map/app sells. Then the only issue is trying to determine how many tour and do not use ACA maps and/or use a used ACA map (already counted) and/or share a map with someone (not counted). Then you just have to determine how many tour in other commercial cross-country groups.
I actually think it would be a very cool idea if groups like ACA, WarmShowers, and the Bicycle Tour Network would send a JOINT survey out to their members (and their customers if a commercial entity) to study this (let some college student do the study). While not a totally accurate number, it would probably cover 75+% of "cyclotourists".
My guess is 1,298,074 people do some form of bicycle touring for at least one night at some point during 2018 in the USA. They are just hard to find!