You know what? It may well have been Bledsoe's battery that was attached to Dabney Maury's brigade. I found this from when Maury was in command of a brigade helping cover the withdrawal from Corinth at the end of May. In Maury's Recollections of a Virginian in the Indian, Mexican and Civil Wars on page 159 Maury says "On the night of our evacuation of Corinth, I commanded the rear guard of the army of the West. The splendid Missouri Brigade, Wade's or Bledsoe's battery, and two fine regiments - one the Third Arkansas, and the other the Sixth Texas - made up my command."

I believe Wade's battery's usual assignment at that time was with Henry Little's brigade so maybe Bledsoe's battery was the one that normally was with Maury's brigade and as they were acting as the rear guard maybe Wade's battery was temporarily assigned to Maury to augment his artillery?