The author Yādava/Śrīyādava is simply telling us that an eminent brahmin named Śrīvatsa was his father and an honorable woman Śrī-bāī (to use our present-day standard spelling) was his mother. Names like Lakṣmī-bāī, Tārā-bāī, Ahalyā-bāī were commonly heard in his time and in his part of the world (cf. Dr. Nagaraj Paturi: “śrībāī /śrībāi / śrībāy is a very much possible female personal name.”). On the whole, scholars were not as strict about the writing of non-Sanskrit words as they were about the writing of Sanskrit words (note, for example, the way the gāthās are quoted and accepted in Kāvya-śāstra works). It was not unusual to write the non-Sanskrit words as one heard them or as the metre required; approximation was acceptable. Therefore the writing of (our expected) bāī as bhāyī or bhāyi need not be viewed as presenting a serious problem. (again. cf. Paturi: “Shortening of the end vowel is not a hurdle …”)

The “ca” in the second quarter of the verse initially bothered me, but there could be justification for it in a preceding verse of the section, if . 

a.a.