There really was no "shipyard" at Bridgeport on the Tennessee River. Here are a couple of quotes from William M. Lamers, The Edge of Glory: A Biography of William S. Rosecrans, U.S.A., pp. 371-72

Rosecrans most urgent problem, therefore, was to reopen short supply routes into Chattanooga. Accordingly, he immediately ordered the construction of four steamboats to be built there, and one at Bridgeport, and the damaged Chattanooga ferryboat to be converted into a transport. He further ordered several sawmills to be repaired, and a dismantled foundry to be turned into a smithy. As September ended, these establishments were producing lumber and metal fittings.

On page 391, Lamers mentions that the Paint Rock had been repaired by October 5th, "although low water prevented its use." As accounts of the Chickamauga Campaign mention frequently, the area had been in a late summer drought which made river travel impossible until heavy rainfall in mid-October. Lamers describes the Chattanooga as "a mongrel, a scow of rough planks, its cabin a canvass-covered room," p. 391.

This reads like what you requested, but it's a very overstated account -
http://www.qmfound.com/little_steamboat_that_opened_the_cracker_line.htm