One site says "Nathaniel BUN was born 23 Mar 1664 in Boston, Suffolk, MA."

Samuel Williams' will attest to a son-in-law named "Bun":

Samuel WILLIAMS was born about 1637/38 in Taunton, Freetown, Mass.. (3291)(3292) He died in Aug 1697 in Taunton, Freetown, Mass..(3293) (3294) This is the date of his will. See transcript NEHGR Oct. 1909:331. Samuel married first Mary Gilbert by whom he had six children. (Mayflower Families Through Five Generations, Rogers). He later married Anna Rogers, Mayflower descendant through Thomas 1, John 2. They had no recorded children. He is called "tailor." His will, "drawn 6, Aug. 1697, inventory presented 31 Aug. 1697, names sons Seth, Daniel and Samuel; daus. Sara Dean, Mary Andros and Hannah Bun. He gave liberty to his wife (unnamed) to live with his son Seth.