bhavānīṁ vandayāṁ cakrur
According to the ācāryas, here the term bhavānvitām indicates that in the Ambikā temple visited by Rukmiṇī, the presiding deity was the goddess, whose husband appeared in an accompanying role. Thus the ritual was properly performed by women.
Śrīla Viśvanātha Cakravartī comments that the term vidhi-jñāḥ may be understood to mean that since the learned wives of brāhmaṇas knew of Rukmiṇī’s desire to marry Kṛṣṇa, the verb vandayāṁ cakruḥ thus indicates that they prompted her to pray for what she really wanted. In this way, like the goddess Bhavānī, Rukmiṇī could be united with her eternal male companion.