There is a way to roughly figure this. Bob Lemke deciphered the figures in the FTC case against Topps in the 60's and found they sold $800,000 worth of cards with gum in 1952. There would have been a small fraction of cards sold without gum as well in cellos and vending, maybe another 3-4%. So lets call it $825,000. They sold their cards to jobbers at 60% of retail, so 825,000/60 *100 = $1,375,000.
The 6 card nickel packs screw it up a bit so maybe instead of multiplying by 100 (a penny per card) we use 110 and get 151,500,000 cards. There are DP's but if you figure the semi highs were produced at half the rate of the low numbers and the high numbers the same as the semi's (which I think was how they did it), then the first four series count twice as much as the last two, so 12 series worth of cards. So approximately 25 Million cards per four low numbered series counts and 12.5 million apiece for the last two. I know the series counts vary but each was a separate run and since they were printed 200 at a time I think the number of individual cards still holds.
So I figure 250,000 of each "slot" then in each of the four low number series and 125,000 per slot for the last two were printed if my math is correct. Roughly speaking. One of you math majors can do the ciphering on the DP's and individual series if you like.
Bob's link, with figures for other years and companies as well:
http://boblemke.blogspot.com/search?q=bowman+sales