Bleach didn't get popular until the anime and even during its biggest years it had serious competition with other series in the mag.
Again, you're overestimating Bleach''s popularity. "The big 3" was a western invention.
With this data:
https://web.archive.org/web/20180310003605/http://www.geocities.jp:80/wj_log/rank/ Bleach volume 12, this is 2 volumes before the anime, it had a first print of 520,000 copies, so Bleach real sales had to be around 500,000 copies because the editorial possibly had to adjust the print run of a series without anime if they didn't want to have too many copies unsold. It's not exceptional or even very good, like, for example, Naruto, that by volume 13 had 800,000 copies in print without anime, but it's still pretty good. The first Bleach arc wasn't popular, Kubo himself admitted that in the first artbook, but Bleach had started increasing its sales, and rankings in the magazine, by itself, with the SS arc, before the anime. Volume 15, 2 months after the Bleach anime started, had 780, 000 of first print, so, apart of more copies in print because of the anime, the manga was surely still increasing its sales in the previous volumes because people liked the arc.
During its run only Death Note had better sales (and Hunter x Hunter, I had forgotten this one), and Prince of Tennis was the only one that it was close (during both series peak), but the volume with the best first print of Prince of Tennis had 1,100,000 copies, and the best fist print volume of Bleach had 1,330,000, so there was still a difference. Naruto best first print was 1,620,000, and One Piece 4,050,000 . So, going by comparisons, rather it would be the big 1