Shulchan Aruch Orach Chaim 492 discusses the custom some have to fast on Monday, Thursday and Monday (BaHaB) following the months of Nissan and Tishrei. Rama in his gloss notes that the custom is to fast starting from the first available Monday of the following months (i.e. Iyar and Marcheshvan). (I assume he means to exclude where the first Monday of the month is Rosh Chodesh.)
Now, consider a case where Rosh Chodesh Iyar (say) is on Friday and Shabbat. I would have thought that BaHaB would start on the first Monday in Iyar (the third of the month).
However, Mishnah Berurah 492:3 implies that BaHaB actually starts the following Monday (the tenth of the month), writing that on the Shabbat following Rosh Chodesh (in our case the eigth of the month) we bless those who will fast BaHaB, and BaHaB then begins on the following Monday.
Why is this the rule? Is there a problem blessing those who will fast BaHaB on Shabbat Rosh Chodesh, such that the blessing, and thus BaHaB itself must be pushed off by a week? What would the problem be?