I suspect your man served with the 2nd Battalion Kentucky Mounted Rifles

Two Civil War battles were fought in Cynthiana. The first, at Licking Creek on July 17, 1862, was part of Gen. John Hunt Morgan's "First Kentucky Raid." The Federal force of 500 soldiers was defeated by Morgan's 800 Confederate soldiers and Cynthiana was captured. The Battle of Cynthiana took place on June 11-12, 1864 and consisted of three separate battles in which the Confederates were defeated, thus ending Morgan's last raid into Kentucky.

These are the only two W. Bowens I found in Kentucky units.

William T. Bowen, Private, Company D, 1st Battalion Kentucky Mounted Rifles, enlisted October 22, 1861 at Prestonsburg by Lt. Thomas for 1 year, left sick at Holston Springs, March 3, 1862, recorded present on the May/June, 1862 muster roll, discharged November 20, 1862

............

William Bowen, Private, Company B, Johnson's Battalion, Kentucky Mounted Rifles,* enlisted October 12, 1862 at Fleming County, Kentucky for 3 years, recorded November 30, 1862 as having served 22 days extra duty Blacksmithing, last recorded present February 28, 1863, no further company B records

* This company subsequently became Company B, 2nd Battalion Kentucky Mounted Rifles

[Note, this regiment suffered at least one wounded 6/13/1864 at Cynthiana, Ky. Sources used by Historical Data Systems, Inc.- Confederate Kentucky Volunteers War 1861-65]

M319: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Kentucky