The roster of the 1st Choctaw & Chickasaw Mtd Rifles shows:

Bull, George W.
1st company I
Age 19
Enlisted June 2, 1861 at Ft Arbuckle CN (Chickasaw Nation)
and on the roll Aug. 31, 1861.

Company I of the first organization became Company E of the 29th Texas Cavalry when their 1 year enlistment was up.

Many of these men were originally McKittrick's Company of Denton County Rangers, Texas State Troops (Texas militia, not Confederate States troops). By enlisting in the 1st C&C Mtd Rifles, they could be used outside the State of Texas. The Indian units could not ordered outside their own country without approval of the tribal government.

I'm sure Patti Adkins-Rochette will see this post and confirm for us whether George and/or Tarlton Bull were originally in the Denton County Rangers (and correct me if I'm misstating any of this).

In mid-1861, the Texas State Troops were in the Choctaw & Chickasaw Nations at the request of the governors of those nations and with the approval of the governor of Texas.

Civil War Soldiers and Sailors System at http://www.itd.nps.gov/cwss/soldiers.cfm
shows

Tarleton D. Bull (First_Last)
Regiment Name 29 Texas Cavalry
Side Confederate
Company E
Soldier's Rank_In Private
Soldier's Rank_Out Private
Alternate Name
Notes
Film Number M227 roll 5

Note that he is also in co. E, the company to which many (~47) of Co. I, 1st C&CMR, reenlisted.

You did not have to be a citizen of an Indian Nation to be in one of its military units. These men were generally non-Indians from North Texas. Also, you don't have to be a particular "race" to be a citizen of an Indian Nation any more than you have to be a particular race to be a citizen of the US. There were many white and mixed-race "naturalized" citizens in the Nations of the Indian Territory.

The two battles you mention...

Elk Creek is another name for the battle most commonly known as the Battle of Honey Springs, the largest engagement in Indian Territory, July 1863.

Cabin Creek most likely refers to the Second Battle of Cabin Creek where, in 1864, the Confederate Indians and Texans captured a US supply train (wagon train) at Cabin Creek Crossing on the military road from Ft Scott KS - Ft Gibson, Cherokee Nation. There was an earlier battle (May 1863) in which the Confederates were repulsed (i.e., First Battle of Cabin Creek) and many skirmishes around the same location.

The records in the Indian Territory are incomplete and virtually non-existent by 1864 so a name missing from the rosters is not proof positive a person did not serve at some time in a particular unit.

Ken