Based on Rashi Eruvin 25b, Rav Bibi is the same person as Rav Bibi bar Abbaye.
Serving food to Rabbi Ami and Rabbi Asi: Shabbat 74a
Rav Nachman said that Rav Bibi's daughters needed heavy depilatories because of his alcoholic consumption: Shabbat 80b
Rav Papi said to Rav Bibi, in response to an idea of Rav Bibi's, "Because you come from people whose lives were cut short, you say words which are cut short (have no legs)" [Alternate reading: "Because you come from great people, you say great things"]: Eruvin 25b
Rav Yosef taught a lesson in the name of Rebbe. Rav Bibi said, "Don't listen to him. I taught him that in the name of Rav Ada bar Ahavah, and I used the word 'Rabim.'" Rav Yosef exclaimed, "Master of Abraham! 'Rebbe' was switched for 'Rabim!': Eruvin 75b