"So Bde stands for Brigade?"
"He was a brigade Commissary Dept Quartermaster?"
You stated that he was assigned to the Brigade Commissary depart. What his exact duties there would have been is not known. A quartermaster usually was an Officer who had a detail of men working under him. You did not specify that Morgan was a Officer. But if not he would have worked under a Commisary Quartermaster.
"Would Morgan likely have remained in camp at Pine Bluff while the unit fought in different locations?"
It is my guess that is why Morgan was not captured at Arkansas Post with the majority if the 19th Arkansas. If he were assigned to the Commissary Department he may well have been at Pine Bluff doing his duty of forwarding supplies to the Fort at Arkansas Post.
The Commissary department worked a various levels. One Commissary Depots was at Sulphur Springs/Pine Bluff until August 1863 when the post was abandoned except for a small hospital staff and garrison. The remainder moved to Little Rock.
The Commissary Depot at Pine Bluff was important because it was the head of a roads complex that came from Napolean and Gaines Landing on the Mississippi River. And the Pine Bluff to Monticello, to Monroe, La. to Vicksburg roads. The confederates were able to use all of these roads to ship military supplies from the east into Arkansas. It recieved military supplies such as shipments of weapons, small arms and field artillery and munitions. As well as gathered foodstuffs from the farms along the Lower Arkansas River valley and forwarded most of these supplies to Little Rock. In some cases foodstuff like corn and cattle were shipped to Pine Bluff for troops there from Texas and Northwest Arkansas. Pine Bluff was also a point where wounded soldiers from the eastern theater returned to on their journey home on furlough. So this depot was quite a crossroads of military traffic and supplies.
The main Commissary Depot for the entire state of Arkansas was at Little Rock until the fall of Little Rock in September 1863. When it moved to Old Washington, Arkansas. These were by no means the ONLY depot. They were scattered wherever they were needed and were moved from time to time.
Usually Commissary Department troops did not as a rule become involved in frontline action. Unless for example they were involved maybe with a supply wagon train that came under attack.
Remember that these are generalizations and that individual services of particular troopers like Morgan Griffith are as varied as the soldier himself was.