General Herron arrived in Alexandria on June 2, 1865, aboard the steamer Ida May, and left there headed for Shreveport on the afternoon of Sunday, June 4. Sometime before June 9, Herron had his headquarters established in Shreveport. So, Herron and his troops probably arrived in Shreveport on the 6th or possibly as early as the 5th of June. Maybe someone else can get a little more specific. (Below is a link to a New York Times story, dated June 9. The other information is from the deck log of the USS Ouachita, which did not go above Alexandria.)
http://www.nytimes.com/1865/06/11/news/war-southwest-occupation-alexandria-shreveport-twenty-two-pieces-artillery.html