I've managed to get a very rough estimate of battlegroup size by comparing the ratings in groups that have less than 5000 teams. Basically I compared 10 battlegroups for 3v3 and noted the percentage of teams above 1499 1600 and 1700 rating. Those turned out to be pretty standard across the board in all of the observed ladders (roughly 44-46% for >1499, 22-25% for >1600 and 12-14% for >1700).
Keep in mind I only checked about 10 3v3 ladders so there's a chance this won't translate well to 2v2 and 5v5.
I'd do some more research but I can't browse the armory for more than a minute without firefox crashing

Also, maybe someone that is actually good at math can do a better job.
Anyway how this can be used... look for the ranking of teams rated 1700 1600 and 1499 in your battlegroup, divide by the percentages given and you should have a VERY rough estimate of total size.
Edit: Using these numbers on the OP battlegroup (Bloodlust-US) I'd guess there are roughly 7500 teams in 3v3 and 15000 teams in 2v2.