All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The scholars differed in opinion about the issue of the waiting period of a woman in Khul' (asking for divorce in return for compensation). Some of them act according to the narration which you referred to in the question, that a woman in Khul' should observe a waiting period of the duration of one menstruation; this is the view of Ibn Taymiyyah . However, there is a controversy about the chain of narrators of the above narration; some scholars classified it as authentic and others classified it as weak. On the other hand, the majority of the scholars are of a different view; their evidence is the saying of Allaah (which means): {Divorced women shall remain in waiting [i.e. do not remarry] for three menstrual periods.} [Quran 2:228]
The waiting period differs according to the state of the divorced woman. The waiting period of some of women are calculated by months, and for some others they are calculated by three menses, and so forth. For more, please refer to Fatwa 82929.
Allaah Knows best.