I suspect that he died in a hospital within the city of Mobile. There were at least two hospitals within the city, Ross General and Wayside. The National Archives does not hold registers of patients for this period. Perhaps, the Alabama Archives may.

There is also the possibility that his father removed his remains for burial in their local cemetery. I have not been able to locate their home through Ancestry.com Federal Census'.

S. J. Bell, 20 year old Farmer, born in Jefferson County, Alabama, enlisted as a Private in Company G, 18th Alabama Infantry July 29, 1861 at Jonesboro, Alabama, present at the November 30 muster, at Camp Gov. Moore, died in hospital December 15, 1861, his father Amon Bell filed claim for his effects October 18, 1862, the regiment was stationed at Camp Gov, Moore near Hall's Mills*, 11 miles from Mobile, Alabama during December 1861

M311: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Alabama

* Hall's Mill is located some 5 miles up Dog River, approximately 9 miles SW from Mobile