The Blue Hat and the Red Rose by Lynn Forest

Union Army Major Charles Morrow has been ordered to escort the daughter of a well-connected Ohio couple from the recently captured town of Cynthiana, Kentucky to her parents’ home. Along the way, he must protect her from remnant bands of Rebel soldiers and hostile Confederate sympathizers. He does not relish the assignment, but at least the journey will take him to within a few hours ride of his own homestead.
Emily McAllister enjoys spending much of her time with her aunt and uncle in their Cynthiana home. Emily is a pacifist, and abhorred the violence that placed Cynthiana back under Union control. To Emily, there is never an excuse for resorting to bloodshed among civilized members of society. She takes great umbrage at the notion that an armed escort has been sent to take her safely home, and steals his horse and takes off for Ohio.

When the Major finally finds her, he arrives just in time to save her from some harsh questioning from a group of green Union soldiers who were convinced that they had captured a spy. Emily experiences some well-deserved discipline from the Major before they travel on. Along the way, there is more danger, and more sabotage of the Major’s reliance upon military skills to keep her safe. But Emily soon finds both her bottom and her emotions smoldering.