From the wording of your query, it seems that you are assuming that Mrs. Sherman came to visit in August 1863 by using the railroads from Holly Springs down to Jackson, and Jackson westward to Clinton crossing the Big Black River Southern Railroad Bridge. Bovina Station was located west of Big Black River not quite half way to Vicksburg. It would be interesting to know that she did travel from Memphis through Holly Springs to Grenada, and down to Jackson on the Mississippi Central.
It is more likely that she arrived by river at Vicksburg, and took the train out to Bovina from Vicksburg. I believe that Sherman's headquarters were moved there after the siege, or they had found a home intact that they could use for the visit, or both.
You asked: >>> Was the RR between Bovina-Clinton ever closed for an extended period some time after Aug 63 and not reopened until Oct 65? <<<
Immediately following the surrender of the Vicksburg garrison on July 4, 1863, General Sherman was sent to retake Jackson which was then occupied by General Johnston's forces. Sherman used the Southern Railroad to transport artillery and ammunition out from Vicksburg. The Federals set up a siege perimeter around Jackson and mounted siege guns. General Johnston learned on July 16th that a train load of box cars carrying artillery ammunition had arrived from Vicksburg to support these siege guns, and ordered his forces to withdraw from Jackson that night.
The forward base for Johnston's forces following this retreat was Morton's Station on the Southern Railroad east of Jackson. It has been my understanding that Sherman's forces withdrew back towards Vicksburg and that in August 1863 the unofficial boundary for the Federals occupying Vicksburg was the Big Black River. In October 1863, Loring's Division was moved back through Jackson and up the Mississippi Central railroad to Canton where they spent the winter of 1863/1864.
When Sherman launched his Meridian Expedition from Vicksburg in February 1864, Loring was ordered back from Canton and withdrawn into Alabama. According to Robert C. Black, III ["The Railroads of the Confederacy" (Broadfoot Publishing, 1987)], Sherman destroyed 51 railroad bridges and 4 miles of track on the Southern Railroad. The Confederates reoccupied Jackson and the Southern Railroad was operational as far west as Brandon Station by May 7, 1864. How much of the railroad between Clinton and Big Black Bridge was destroyed was not stated in Black. It is not likely that the Confederates restored it.
Upon completion of the Meridian Expedition (or Raid), Sherman withdrew his forces behind the Big Black River and shifted his attention to Chattanooga with his eye on Atlanta. A "flag of truce" camp was maintained at the Big Black River thereafter and it became a delivery point for the exchange of prisoners of war in the spring of 1865.