Bibby Bush is believed to have been the son of Richard Bush who died in Edgefield District, SC in February 1803 because he (and Prescott Bush) administered Richard's estate. It's not known if Richard's wife, Mary, who is believed to have died sometime during 1800-1803, was Bibby's mother. Mary may or may not have been Richard's first wife, and she may or may not have been Mary Prescott, daughter of William Prescott.
Bibby's wife at the time he died, Mary, may or may not have have been his first wife and may or may not have been a Herrin. Bibby had children over a twenty to thirty year time span and may have had worn out more than one wife. This being said, it's true that Bibby once had land near Joshua Herring in North Carolina, and it's true that he had a late in life son named Herrin.
There's lots of information about the Bushes of Edgefield in this forum, some good and some bad. Horace Satcher's posts, in particular, are excellent.