Well, being so bat-focused my first instinct is to look at it from his point of view, and Bruce being Bruce will never be wholly comfortable being that close with someone who isn't a mortal human like he is. Especially when you factor in how much death has played a role in his life, oddly enough. Although there is the possibility that Clark or Diana could die, I think he would have a hard time reconciling himself with being partnered with someone who is immortal.
It's really messed up, but I think he would be more loving and interested in someone whose life could be cut short, because he knows how precious (and potentially brief) life can be. (Which, ironically is also what makes him drive people away, because he's scared of losing them.) If he was with someone immortal, he wouldn't have to worry about them as much, and I think a part of him would start to resent them for it. "Why do they get to cheat death but my parents couldn't?" Their lives and his life tend to be governed by different sets of rules, and blending them raises all sorts of problems.
In short: Bruce would fuck it up somehow. He's better suited to someone of approximate equal strength.
the difference between, say, Rama and Trevor Barnes proves that it's a problem for writers, but that's on the writers, it's not Diana's hang-up.
Well, that could be boiled down to most people being comfortable with a couple of equal power or the guy being stronger, but the woman being stronger is somehow strange and off-kilter.
even though Bruce's distrust of metas is part of the fundamental core of his character from hating Starfire on out.