The distance between Brownsville and Fort Pillow is about 35 miles. This from map found in "That Devil Forest." The book does not mention the death of Major Bradford.
However, I found this:
Maj. Booth, of the regular army, was in command. He was killed about 11 o'clock by a sharpshooter, when Maj. Bradford, of the Thirteenth Tennessee Regiment, took command. Maj. Bradford was taken prisoner and killed, near Judge Green's, some 6 miles from the fort, while a prisoner