The regiment left Bridgeport on August 20, arriving 3 days later at Chattanooga, a distance of 30 miles. He was left at a private house on August 22, if I'm reading correctly.

Looking at the Official Atlas accompanying the Official Records, Plate 35- 4 & 5, I suggest the route they took was North to Jasper, thence East, North of the River, over the Stage Road to Chattanooga, a total distance I measure at about 30 miles.

Now, I would suggest that he was left at one of the the private homes on that route, from West to East: Wash Pryor, Dave Kelly, Widow Hall, or Bob White.

.......

Left sick on the March [at a private house] from Taylor's Store, Ala. to Chattanooga, Tenn. by order Brigade Surgeon Aug. 22, 1863

Company K, Record of Events

Stationed near Chattanooga, Tennessee, July-August 1863.
July 6.— Arrived at Chattanooga, Tennessee. Distance, about
100 miles.
July 12.— The company went by railway to Bridgeport,
Alabama, where it remained on picket duty.
August 20.— Returned to Chattanooga by a very slow march.
August 23.— Arrived at Chattanooga. Distance, thirty miles.
August 30.— Moved camp ten miles up the Tennessee River,
where it now is on picket duty.
Stationed at Missionary Ridge, Tennessee, September-October
1863.