Son of Joel Bassham and Sophia Asbury.

There was a William Bassham who was suspected of being a guerrilla during the Civil War. He was sentenced to be shot on Aug 11, 1863 at Independence, MO, but escaped during the Battle of Independence. After McCorkle and 9 other guerrillas rescued him, he joined the band. Before the war, he was a stage coach driver along the Santa Fe Trail, hired by the U.S. government.
Source: Roster of Quantrill's, Anderson's and Todd's Guerrillas website.

("Quantrill's Raiders were the best-known of the pro-Confederate partisan guerrillas (also known as "bushwhackers") who fought in the American Civil War. Their leader was William Quantrill and they included Jesse James and his brother Frank.")

I do not believe the two were the same man. As proven by the Census, Wm. V. Basham from Carter County was only 13 in 1860. He would have been too young to be a stage coach driver before the war, or be involved with Quantrills Raiders.

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William Basham in the 1860 United States Federal Census
Name: William Basham
Age: 13
Birth Year: abt 1847
Gender: Male
Race: White
Birth Place: Kentucky
Home in 1860: Blue, Jackson, Missouri
Post Office: Blue Springs
Dwelling Number: 798
Family Number: 738
Household Members Age
Joel Basham 47
Sophia Basham 47
Edmund Basham 26
Solomon Basham 21
Joel Basham 19
John Basham 17
Ann Basham
William Basham 13
Armatha Basham 12
Paulina Basham 9

Wm Basham in the 1870 United States Federal Census
Name: Wm Basham
Age in 1870: 24
Birth Date: abt 1846
Birthplace: Kentucky
Dwelling Number: 651
Home in 1870: Township 48 Range 31, Jackson, Missouri
Race: White
Gender: Male
Post Office: Lees Summit
Occupation: Laborer
Male Citizen Over 21: Yes
Household Members Age
Jas Basham 29
Martha Basham 23
Cora B Basham 11/12
Mgt Hylton 44
Jno H Hylton 15
Wm Basham 24

William Basham in the 1920 United States Federal Census
Name: William Basham
Age: 73
Birth Year: abt 1847
Birthplace: Kentucky
Home in 1920: Pike, Carter, Missouri
Residence Date: 1920
Race: White
Gender: Male
Relation to Head of House: Father-in-law
Marital Status: Widowed
Father's Birthplace: Virginia
Mother's Birthplace: Virginia
Occupation: None
Able to read: Yes
Able to Write: Yes
Neighbors: View others on page
Household Members Age Relationship
Alexander Zinn 47 Head
Cora Zinn 41 Wife
Flossie Zinn 16 Daughter
Earl Zinn 11 Son
Howard Zinn 2 Son
William Basham 73 Father-in-law