"are there any books on the Civil War at and around Pine Bluff?"

Not anything that is accurate. Most of the books written about Southeast Arkansas deal with Units, like John Wrights Cavalry, or indiviual battles like Arkansas Post. There are a number of articles written about the Battle of Pine Bluff, but most are just rehashes of the OR's and Maradukes reports.

"was there a fight or action near Pine Bluff on or around July 11, 1864?"

The primary mission of the Union Garrison at Pine Bluff, from September 1863 until the end, was to control the country side to prevent an attack on Little Rock. Hence there were almost constant patrols and expeditions by the Union Forces to Mt Elba, Warren, Monticello, South Bend etc.

On the other hand there were also constant probes by the Confederates around Pine Bluff to keep Powell Clayton bottled up as much as possible until well into 1865.

In 1862 and 1863 the Confederates use Pine Bluff in the same manner as a counter to the Union forces at Helena and the on the Mississippi River and as a support to Arkansas Post.