From what I've read, Richard A. Inge served as Captain of Company B for the majority of the war until Captain Inge and First Lieut. T. Otis Baker were wounded July 28, 1864 at the Battle of Atlanta.
Four months later, Captain Samuel B. Watts (CO H) commanded Companies B & H at the Battle of Franklin, November 30, 1864. Watts was captured here and spent the rest of the war as a POW.
TOB is listed as Captain in one of the three companies formed from the remnants of the 10th. that were consolidated into the 9th. Regiment.
Sources:
http://mississippiscv.org/MS_Units/10th_MS_Inf.htm
http://www.natchezbelle.org/adams-ind/southron.htm