James,
I have read many things about Burnside over the years and I always saw him as a somewhat timid fellow who really did not desire a command.
I have from time to time read about Knoxville in that I have a somewhat interest in that part of the war. My Great Grandfather was with Sherman at Missionary Ridge and after that battle as you know, He (Sherman) and his troops were ordered to the relief of Burnside. In the back of my mind I have always thought that there is old Burnside in trouble again. Then recently I have been re-reading "The BLue and Gray" by Henry Steele Commager who was not necessarily an "expert" on the Civil war but was a very educated man who put to gether this book that was origionally a two volume set of what I would call Documentary History that lets historical events be explained by the participants of the event and that is what he has done in this book. Let those involved, both BLue and Gray, both Officer and Enlisted man tell us how it was through their eyes. The account that made me start to see Burnside in a different light was a report by one of the young officers who explains that Burnside was not retreating but was with drawing in a measured fashion in the hopes of drawing Longstreet farther from Chatanooga so that if he was needed back in Chatanooga he would be to far away to respond in good fashion to be of any help to Bragg or who ever was in need of his troops.
I would think that the book is available at your local library.
Frank