You have access to the Official Records of the War of the Rebellion, which will make your project much easier.
http://digital.library.cornell.edu/m/moawar/waro.html
Being assigned to the command formerly led by Brig. Gen. Abram Buford, the 57th Alabama Regiment became part of Col. Thomas M. Scott's Brigade, William W. Loring's Division. Just follow Scott's Brigade and/or Loring's Division. If you limit yourself to specific regimental references, the trail will quickly go cold.
From the O.R., series I, volume 32 --
Part 1, page 808
Major-General WITHERS, February 27, 1864. Selma:
Order the Alabama regiment of Clantons brigade, now at Selma or Montgomery, to this point as early as practicable.THOS. M. JACK, Assistant Adjutant-General.
Part 2, pages 604 and 659, list the regiment with Scott's Brigade on March 10th and 20th. According to page 815, same part, division HQ was located at Montevallo AL, Apr. 24, 1864. An inspection of the division at that point was completed on Apr. 29th, page 854.
Skipping to the O.R., series I, volume 38, we have the following from part 4, page 679 --
ROME, May 8, 1864.
General W. A. MACKALL, Chief of Staff:
Scott's brigade, of Loring's division, was within twenty-seven miles of this point at 11 a. m. today. It will be up to-morrow evening.W. K. BEARD.
HEADQUARTERS BRIGADE, LORING'S DIVISION,
On march, four miles south of Jacksonville, May 8, 1864. (Via Rome.)
General JOHNSTON:
My command left Blue Mountain this morning at 7 oclock en route for Rome. I am instructed to say that the entire division will follow as early as possible.THOS. M. SCOTT,
The campaign report for Loring's Division (vol. 38, part 3, page 874) mentions the arrival of Scott's Brigade at Resaca GA on May 10th.
From this point you may continue to use the Official Records as well as records of other regiments assigned to Scott's Brigade. For instance, Bloody Banners and Barefoot Boys: a history of the 27th Regiment Alabama Infantry CSA: the Civil War memoirs and diary entries of J.P. Cannon, M.D. by Noel Crowson and John V. Brogden, page 133, mentions that the 27th Alabama
took the train to Blue Mountain near Anniston, Alabama, marched through Rome, Georgia, to Kinston where they took the Chattanooga Railway to Resaca. There, on the 11th of May, the troops met General Johnston's army retreating from Dalton.You can pick up J. P. Cannon's diary entries which begin on May 13th.
Looking for other elements of this brigade, you'll find a description of the misidentified flag of the 57th Alabama here --
http://www.rhsresearch.org/Flags.htm
I spoke with a descendant of Lieut. Col. W. C. Bethune at church last night and will encourage her to post on this board.