I am taking a stab at this because I have a few clues, and I know a little bit about a handful of Kentucky families.
First of all, on the 1880 St. Charles Co., census, Neville age 15 and Eugene age 10 BULLITT are living in the household of R. F. LUCKETT, and are listed as his nephews.
There doesn't appear to be another Bullitt-Luckett marriage, so it is highly probable that these are the sons of William S. Bullitt and Belle Luckett.I think that William S. Bullitt might be the son of Alfred Neville Bullitt and Minerva Beckwith.This couple migrated to St. Louis MO around 1840.Minerva Beckwith is the daughter of John William Beckwith and Mary Floyd Smith.I believe Henry Fenton Luckett is the son of Levin Luckett and Letitia H. Peyton of Loudoun Co., VA.
If Neville and Eugene are indeed the children of this couple, then William S. is of the line of Cuthbert Bullitt m. Ann Neville.There are two possibilities:1) he is the son of Alfred Neville Bullitt as stated above, or 2) he is the son of William Neville Bullitt and Virginia Anderson.They had a son named William A. Bullitt b. 1840, who was an attorney in Lawrenceport, IN at one time.William A. Bullitt is on the 1880 census in Jefferson Co. as single.