If the world is destroyed, so is Gotham. Batman learned that when he tangled with Ra's Al Ghul. After fighting the Imperium, he realized that the world will be threatened on more than one occation, and the random assortment of heroes that gathered together couldn't handle it.
He had met Superman before. A superpowered boyscout the people turned into an icon. Green Lantern was competant, but he answered to powers he wouldn't question. Hawkgirl was perhaps intriguing but seemed to punch first and ask questions later. Flash was a show-off and an idiot. The Amazon and the Martian were too new to this world to be able to protect it. Batman signed on to fund the team and to watch them watch the world. He would only be a part-timer because Gotham can still be destroyed even if the world is saved.
So he helped them. Batman's own family, Batgirl and Robin, served directly under him. These other heroes had their own lives. He would remain professional with them. They fought and they even broke up for a short time.
It wasn't long before Batman began to enjoy his place in the team (as much as he could anyway). He experienced kairumption with Wonder Woman. When Superman died, he finally admitted to himself that he did respect the Man of Steel.
The Justice League were now equals. Superman had as much a burden of protecting the world as Batman did. Hawkgirl was just as smart a detective. Batman was honored to serve among them, and it felt good. The more he worked with the League, the more he looked down on Batgirl and Robin. He always had to watch them and hold their hands. He ended things with Batgirl before they got too serious and began a flirtation with Wonder Woman, which only got stronger when he told her his secret.
Despite what happened with Hawkgirl, Batman was comfortable with telling the League who he is. He voted her out of the Leauge (I think) and began to question his mission. He and the others agreed to expand their ranks, and Batman would take an active role, recruiting other heroes he had met.
Then the unthinkable happened, Joker kidnapped Robin when the League was at its weakest. There was no one he could call to for help (everyone was either recruiting, in space, or otherwise unavailable), and when he found his sidekick, it was too late. Tim's mind was damaged, and his crusade was over. Batman decided he'd never take on another partner. After seeing his dark authoritarian twin, maybe he shouldn't be completely trusted to guide another like he did before. He took away Barbara's costume and set up a display in the Batcave. He'd let Nightwing stay in his own city and find his own way. Barbara eventually reconcilled her two identities and went into the field of law enforcement. Tim would lead a normal life some day.
Batman helped the League recruit. He brought in the likes of The Creeper, Wildcat, Zatanna, Huntress, Etrigan, and even helped convince Green Arrow to join up. Losing the Batfamily left him confused. He allowed himself to get close to Superman, who he knew wouldn't get hurt, and even celebrated his birthday (although his thoughts were on regressing back to being a boy and regaining his parents). With Wonder Woman, however, he firmly told her why he wouldn't date her, despite his feelings for her. He became Green Lantern's romantic confidant and respected Flash more (possibly after having to deal with bigger idiots, like Booster Gold).
Batman treated Superman and Wonder Woman with even more respect than the public would. He began to question whether or not their power was too great. He knew what the other Superman did and saw how his own Superman dealt with Doomsday. His fears were put to rest when his teammates decided to willingly hand themselves over to the authorities. It was stupid because they would let the real problem go unconfronted, but it was all Batman needed to know to convince himself that this team wouldn't turn into the Justice Lords.
Batman did something he never could around his old family, he relaxed. He went to Flash's celebration and found himself joking with Superman. Where he would once call Captain Marvel naive, he appreciated his bright attitude. Rather than make everyone else darker, the team made him a bit brighter (plus it helped that Joker was definitely dead, not having returned after a couple years). He showed compassion for Ace when she needed it.
Wonder Woman gave up her romance with Batman and pursued Agent Farraday. Batman was okay with this, and by 2009, he came very close to finally uniting with Talia only to lose her. It was unfortunate (as was the Near Apocalypse reducing the number of heroes in the League which was then followed by Alfred's passing away), but Catwoman came around. She gave up her old ways and joined Batman's crusade. Feeling she couldn't compete with Talia's memory, their relationship didn't last.
Batman then began to get older, slower. He watched heroes like Stargirl and Static reach their prime while he was getting out of his. Studying the works of John Henry Irons and Pat Dugan, he created a suit to compensate. He began to resent Superman and Wonder Woman for their eternal youth. He knew it wouldn't be long when he was an old man and they weren't any older than the day he met them. He no longer felt as close to them as he once did.
Batman spent less time with the League until he spent no time with them. He was only a part-timer, anyway, it wouldn't be that much of a loss. Then came the night when he had to give up being Batman because he almost used a gun. When he was forced to be only Bruce, he began to lose his strong will and determination. Another man took over his company, and Bruce was alone for years.
It wasn't until a young punk named Terry McGinnis learned his secret that Bruce got his last chance to have a family he wouldn't push away or leave him behind. Terry reminded him so much of himself it was eerie. He let this kid become Batman. Terry looked up to Bruce like Tim did, but he was his own man like Dick eventually was. There was something different about Terry, he took the Batman legacy and made it his own. Bruce worried about Terry, but he felt secure in feeling that he wasn't manipulating him at all. Terry's presence in Bruce's life allowed him to build the bridges he burnt with Barbara, Tim, and even Dick. He could relate to them as human beings, not sidekicks or children.
Terry remained Batman for years, forging his own destiny and following in Bruce's footsteps. Gotham was safe, and the League had another Batman to respect again. Bruce eventually found out that Terry was his son, but after the initial shock, it didn't change things for either of them. Terry had already been a son to Bruce. Not a sidekick, not just a protege, a son. Bruce lived long enough to see Terry name his first son after him. Bruce Thomas McGinnis. Bruce Wayne left many legacies; this one made him the proudest.