That's a much trickier question than I thought it would be. Bucky is a murderer, and even though he was brainwashed into it, Batman is still the type of guy who would want to bring him to justice for it. So he would probably oppose Cap purely on those grounds. Stories like Heketia prove that he'll go against his own allies if they obstruct his pursuit of a wanted crimimal.
But, although Batman is clearly a big believer in metahuman accountability, as shown by his actions both in BvS and comics such as Tower of Babel, he isn't the type of guy who would willingly give that responsibility to the government. He's seen enough to know it probably wouldn't be a good idea, and besides, he's a control freak who wouldn't easily trust something like that to anyone but himself.
If Batman were to enter this conflict, I can see him opposing both sides for different reasons. He would probably have nothing but respect for Cap, but still try to bring Bucky in for his crimes. As for Stark, I can easily see Bruce taking an instant dislike to him, and he would probably see the flaws in his plan as well. At the same time, he would probably be developing his own checks and balances on metahuman activity, and not all of them with their consent or knowledge.