The history between Batman and Wonder Woman is both interesting and various depending on which media you find them in. Most often, Batman reveres her, as he sees her as a true being of strength and purity with little to no agendas to be had, a rarity for Batman. But also though, he know that he personality can make her a very dangerous person if unchecked and unchallenged.
In fact, it's been stated that of all the Justice League members, Wonder Woman technically is the only one to not have a weakness that he can easily exploit. Thus, he's had to go to extraordinary links to think of ways to stop her if she ever went rogue.
However, more often than not, Bruce and Diana are really good friends. And in the legendary Justice League cartoon, more than friends. Though it could be argued they were never a "true" couple in the show, it was noted many times how Bruce felt for her, and that Diana felt the same.