Based on quick review of O.R. Volume 23 (Part II):

On July 4th General Bragg order Polk to cross his army corps at Bridgeport. Polk replied that had already done so when orders reached him. Brig. Gen. John K. Jackson's Brigade remained on the south bank of the Tennessee River until relieved by Anderson's Mississippi brigade on the evening of July 13th. Anderson's report of July 15th notes some of Jackson's men still guarding bridges at Lookout Creek and near Whitesides Station.

McCook had three regiments in and around Stevenson as early as July 19th. Federal reports of July 23rd mention the rail line being open to Bridgeport, cavalry with a battery being sent there on July 28th. Cavalry returned the following day to exchange shots with Anderson's men on July 29th. Bridgeport seems to have occupied by Federal troops from that point forward, Col. Luther P. Bradley's command arriving on July 30th. The cavalry seems to have been from Col. Daniel M. Ray's Brigade.