Anyone who is interested in the Bahira legend would do well to read Sidney H. Griffith's "Syriac Writers on Muslims and the Religious Challenge of Islam" (published 1994 by St. Ephrem Ecumenical Research Institute, India, as vol. 7 of their "Moran 'Etho" series on Syriac Christian topics). It is not quite as simple as the popular legend goes, and indeed the Christian and Muslim versions differ greatly in their content and meaning/use (as you would expect).
From the sources I've read on the pre-Islamic and early Islamic Middle East, I don't think Sargus Bahira was necessarily the source of Muhammad's warped doctrine (or if he was, his assignment to this or that sect says more about the writer portraying him than anything else). No doubt, he could played a certain role (again, depending on whose versions you're reading), but it seems far more likely to me that the offending teacher would've been an Ebionite
monk, and the Ebionites were Judaizers of varying Gnostic tendencies, not Nestorians.