If you look at the trailer carefully, you are going to see several clues to the movie and what is in store -
1. Yes, Bruce Wayne was in Metropolis when his building collapsed due to the fight with Zod and Superman. Therefore the basis of his hatred for Superman.
2. Zod's body and the Kryptonite was recovered by Lex Luthor, who somehow either clones Superman or has physical control of him. (Why would Superman bow in front of him).
3. Ben Affleck's portrayal of Batman/Bruce Wayne is more fitting to the Frank Miller's The Dark Knight Return's character and the suit is a direct connection to that.
4. Did you catch the Joker's message on Robin's outfit. This movie supposedly takes place after the "Death in the Family" storyline and Robin (Jason Todd) was killed by the Clown Prince.
5. It is being speculated that the message Bruce Wayne received was sent by Jason Todd as the Red Hood. Some say it was sent by the Joker, but the Red Hood angle is more plausible.
6. Zod's body being recovered by Lex Luthor may be reanimated by Luthor but only to turn into the Doomsday beast. Not understanding Kryptonian physiology may do that.
I'm not sure what role Wonder Woman plays here or how she becomes involved in all of this. Maybe there will be some clues in a second trailer.
Whatever the outcome of this movie, this will eventually lead into another Batman movie with either the Joker or Red Hood, the rumored Justice League movie, a third Superman movie or all three. It appears for now, DC has decided to a "darker" road with these characters to distance itself from the Burton/Schumacher/Donner films.