I have found a B.P. Herndon in my line, listed as Bently Prestly Herndon in my grandmother's notes, who was brother to Henry James Herndon.
Henry James Herndon was born in Orange County VA in 1803, and died in 1829 or 1830. He married Elizabeth Templeman circa 1827. They had only one child who was Dr. James Henry Herndon born at Orange County Courthouse Oct 28, 1828 and died in 1868. Henry Herndon was the Executor of Henry James Herndon's estate.
Dr. James Henry Herndon married Maria Louisa Taylor and had one child, Dr. Henry Taylor Herndon (1850-1912), with her before she died with Tuberculosis in 1850. Dr. James Henry Herndon left his son with his maternal grandparents (the Taylors) and moved to TX where he remarried and had 4 more children. Dr. Henry Taylor Herndon was born in Huntsville, MO (Randolph County).
There is a side note in Grandmother's notes that say "A note from letter written by his uncle Thomas Townsend Taylor, Noble, Illinois in 1869 says, 'P.S. Great grandma willed one of her farms to Dr. B.P. Herndon's children the other to Dr. Miller's, all great grandchildren.'"
Seems like it could be a good fit if any of those particulars match. Could the first Dr. Bertley P. Herndon and Dr. Bently Prestly Herndon be the same person?
If your info fits at all, I'd love to have your particulars. Unfortunately, this is all I have referring to a Dr. B.P. Herndon.