Walter Bain/Bayne must be a shadowy character. I don't find any family tree in Ancestry that uses this man's name, and could find him only once, on the 1850 census of Shelby County TN.

Aside from the four names you listed, about sixty-five other Mississippi Confederate service files exist under names Bane/Banes, Bain/Bains, Baine/Baines and Bayne/Baynes. Some must be duplicates or reference cards only, because the 1860 census of Mississippi lists fewer than four dozen men by these names in a broad military age (born 1848 - 1808).

That's still a lot of names and military records for anyone to search.

Guessing that you were interested in men in this group born in either Tennessee or Kentucky, I searched the 1860 census of Mississippi for those choices. There are none born in Kentucky born before 1843, and four born in Tennessee before 1843. These are -

Harvey Bain of Noxubee County, born ca 1835. In 1880 Harvey Bain listed his father's place of birth as NC. In 1850 he is living in the household of Mary and Charles Bain.
William W Bain of Pontotoc County, born ca 1842. He lives in the household of William Bain, born ca 1801 in SC.
Jack Baine of Yalobusha County, born ca 1832. He is a house carpenter with no family in 1860.
William A Bains of Madison County, born ca 1830.

Do you have a different reason for selecting the four men mentioned? I was able to determine that Walter T Bain was born Oct 1844, son of Robertson W Bain (1812 - 1859).