The identified location for Nebraska Death Certificates only has DC's "since 1904." So it will NOT have his wifes, and since it appears he died in 1904, they may not have his.

You probably have his 1870 Census data. I researched it to see where he was living after the Civil War, it also shows pre-Civil war in Missouri.
The 1870 Census of Templeton, Atchison Co, Missouri
Stephen Bayless(sic), age 42(1827/1828), Ohio, farmer
Novella(sic), age 24(1845/1846), OH
Henry, 12(1857/1858), MO
Belle 8(1861/1862), NE
Flora 6(1863/1864), MO
Cynthia 4, MO
Homer, 2, MO.
--In 1880, Novella A, 36(1843/1844); "Steavin," 53 Bayles were at Pleasant Hill, Webster Co, NE
--The 1885 Nebraska State Census: "Steve" age 58, "Lavella" age 42 at Red Cloud Precinct. (Name transcribed as "Bayliss").

There is a Stephen Bayles, buried at Blue Mound Cemetery, Milford, Seward Co, NE. He served in the Civil War, Company E, 35th Missouri Infantry.
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=ba...;

Other records confirm this is the correct person:
--This person filed for Pension on Oct 16, 1884, application 524554, Certificate #331547
--Nebraska Military Roster, June 1, 1891: Stephen Bayles, Private 35th Infantry, Co, E, Red Cloud, NE

The National Archives records for US National Homes for Disabled Volunteer Soldiers:
Stephen Bayles, enlisted August 19, 1862 at Scott City, Missouri. Servied with the 35th Missouri Infantry, Company E. Discharged June 28, 1865, Little Rock, Arkansas. Disability: Rheumatism, since 1873 at Red Cloud, NE. He was born in Ohio, age 72, 6'-2" in height, light complexion, blue eyes, dark hair, could read and write, was a gardener, widower. Nearest Relative, Homer Bayles, McCook, Neb (son). He was admitted into the home on August 1, 1899, discharged on July 21, 1900 at his request. Readmitted on April 1, 1904, discharged Dec 13, 1904, cause: "Dpd. G.O. No. 65." Admission on Order of Colonel Sidney G. Cooke, Manager, Pension #331.547.

Nothing found for Novella.