I remember reading League of One and initially being disappointed. Because it wasn't, as I thought it would be, a JLA story. It was a Diana story. And being the callow youth that I was, I thought, "Oh brother." I read it still, and liked it - but have to admit that most of that boiled down to "Dragons! Gnomes! Naiads!" I was a sucker for mythology and folk tale. Still am.
I can say safely now that I have learned from those days and will one day hopefully soon own a copy. And, by the way, I have to disagree with you on the whole bathing suit thing. Because that scene...hot.
However, as a Bruce fan, I'm going to step up to the plate.
Speaking of her friendship with Clark, I find the contrast between him and Bruce really interesting here. Batman finds out what's up and starts in on her with orders and threats, graduates immediately to insults, and makes an attempt to outfight her and impose his will; only when he finally gets truly desperate does he admit his concern for her or try to reason with her. Superman's first reaction, on the other hand, is "What's going on", followed by one solid hit to get her off his back, followed by "I don't understand, but let me help." Says a lot about them and the way they relate to her.
Well, hmm. Unpowered individual facing a woman who is clearly out of his league, who he knows to be a figure of truth, and who is LYING. Bruce is a damned good liar. I think he can tell when someone else is lying - especially when it's Diana, to whom lying is anathema. By the way, when she lies in that scene during the round table discussion, does she have on the lasso? I thought that would negate any lying. Anyway, as you state, Bruce gets his detective on. Suspicious, he hangs back, and watches Diana just kick Wally into unconsciousness. Now, perhaps if he was more like Clark, he'd go, well hey there Diana, that's awfully unkind of you, mind explaining yourself? And she'd go Sure Bruce and kick him into unconsciousness as well. Also, a Clark-esque Batman would be dead on the streets of Gotham within a day, without question. So he finds this figure of truth, someone he deeply admires, and I think instinctively trusts (hard enough), beating up their comrades. He's by this time figured out that everyone else is out of the game. He's pissed, and he's worried, and...he's BATMAN. Of COURSE he's going to use demanding tones and harsh words. Half, MORE than half of his effectiveness as a vigilante is his ability to play on the psychology of others. And that's what the entire scene with Diana is. He's trying to use her beliefs and convictions as a tool to manipulate her, to give him a fair fighting chance. Because as we all know, on a one on one basis, Diana will take Bruce any day. Toying with her mind is the only tool he has. And he knows that she's broken up about what she is doing, so he tries to goad her into making a mistake. Which, you will note, she realizes. Clark's approach works because he's damned invulnerable and because he is honest-to-God sweet and warm as butter. I also happen to think the reason that Bruce even manages to escape the lasso is because he is trying to introduce doubt into her mind. That's if we take the view that the lasso is an extension of herself and her strength - I'm not sure what use the writer has in mind for it, beyond Truth detector.
Basically, I think your characterization of Bruce is off base. He comes into this fight knowing that she's already taking out their comrades and thinking the worst. He can't afford NOT to. Clark comes in as naieve as you can be. Do I think that would necessarily change Clark's approach? No. He's trusting, and nice, and also, did I mention, INVULNERABLE? Mind you, he wouldn't be tricked into getting sucker-kicked by Diana if he'd known that she was knocking out the entire JLA.