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The guy blowing himself up was the final straw. It started from the Zod vs Superman fight. Something you have to remember is that we, the audience, know that Superman was the good guy. Some people in Metropolis see him as a hero, but look at the beginning of the movie. Bruce tries to get his building evacuated and hundreds of people would have been killed, just from that building collapse alone. He finds one of his employees who had his legs crushed and then saves a little girl. The girl is obviously the daughter of another one of his employees, an employee that died in the building collapse.
Man of Steel is the first time that world ever saw a, as they call them, Meta-Human. Wonder Woman was around in the early 1900s but it's likely her abilities were only known to a few people and nearly 100 years later any tales of those would have been long forgotten or dismissed. So Superman is the first world wide known Meta-human and as people see it he has the powers of a God. For a Bruce Wayne that has obviously been Batman'ing for a long time and has gone through some hell (the costume of an obviously dead Robin and the possibly bombed out Wayne Manor are evidence of that along with how he acts) this terrifies him. Bruce never looks at the bright side of things. He is paranoid, he is insane. Bruce controls his insanity by being Batman and fighting villains but at this point in his career he's clearly barely holding it together. So he sees Superman as a potential threat. Bruce believes, as he tells Alfred, that if there is even a chance that Superman might turn on them (humanity) then they need to take him out. The movie is drawing clear parallels between Bruce and Lex for most of the movie. Lex is also terrified of Superman. For different reasons but he still doesn't believe Superman is a good thing to have around.
Speaking of Lex. At some point Lex figured out who Batman is and then used the incident in Africa to confirm Superman's identity. From there he set things up so the two would meet first in their disguises (Clark Kent and Bruce Wayne) and then later. You can see when the truck pulls into Lex's warehouse that Lex is happy. Batman attacked and was stopped. As we see he was stopped by Superman, who gave Batman a warning. This only further drives Bruce into his madness. I need to rewatch the movies and see what the returned checks from the guy said, but it was the final tipping point for Bruce. Superman flying away unharmed while dozens, if not hundreds, of people all die probably triggered some PTSD from the Metropolis battle. Bruce would have seen it as Metropolis all over again.
As for Superman arresting Batman. How? Outside of that big chase through the streets it would be hard for Superman to find Batman. Superman doesn't know his identity until Lex points it out so it's not like he can knock on Bruce's door and drag him in. Batman also operates in the shadows most of the time and Superman only hears about what happens after the fact. He can't use his X-ray vision to find a Batcave he doesn't know exists and with scrutiny on him trying to interfere in everything it wouldn't look good if he kept flying around Gotham watching every single person and place until he managed to find Batman.
Superman DID try talking, Batman refused to listen. Batman was too far gone a that point. There was no reasoning with him. It took being reminded of his mother "Save Martha" to snap him out of it. On top of an explanation that Superman's mother is also named Martha. It brought Batman back to his senses and made him realize how far he had gone as well as Lex's manipulations.
