Batman's presence was first made known to the crew during the climactic stand-off between conflicting factions following the events of the Yeerk Trial, though it has since been made clear that he has been on the ship for a far greater stretch of time. He remains a relatively elusive member of the crew, surfacing only when a task needs taking in hand, or, as in most cases, a crew member needs shouting at. It will come as no surprise that most of his working relationship with the crew's internal command structure is one of begrudging reluctance. He continues to perform the majority of his duties, whether self-appointed or otherwise, without sanction and if at all possible, unnoticed.
As one of the ship's two Metahuman/Non-human liasons, he has attempted to approach the crew with a diplomatic stance, but his demeanour suggests that he pursues a different agenda entirely. Quite what he's up to is anyone's guess, but his enemies had better be watching him as closely as he is them.
Neuropathy - Batman generally hangs out in the department he founded, working on the myriad of corrupt and missing data entries in Stacy's surface programming. De facto leader, (though not all of his staff acknowledge it) the most likely opportunity for a character to run into the Batman are if they're on his team.
Sensoriums - When not working, eating or resting, Bruce is most likely training in the ship's simulated dojo. Keep your wits about you if you find him in here because there are probably simulated ninjas ready to run you through with katanas at every turn.
Batcave - Not that anybody knows where it is, at least not yet. Currently unfurnished, but he plans to amend this first shore leave he gets.
Hangar - Batman loves his toys, and one of the ones that can fly is stashed in the hangar. Redesigning it for out-of-atmosphere flight has become something of a pet project and he can often be found working on the Batwing whenever the more obligatory tasks around the ship prove too frustrating.
Bridge - Not exactly a frequent sighting, but as one of the crew's senior tactical officers he's occasionally required to weigh in on a given situation.
Clark Kent - BFF, for reals.
Damian Wayne - Bruce's biological son, one that he has had virtually no contact with. Currently very wary of the havoc Damian's League of Assassins upbringing is likely to wreak.
Diana Prince - Alias Wonder Woman. One of his oldest friends and a trusted confidante, Diana is the person most likely to talk Bruce out of doing something stupid.
Dick Grayson - Former ward and partner in the Fight Against Crime. Though their (or more specifically Bruce's) methods have put them at odds in the past, they still consider one another family. Their relationship is both brotherly and like father and son. Trusted implicitly.
Guy Gardner - One punch. One punch!
Indigo - Possibly secretly evil. Keeps an eye on this one.
Jaime Reyes - The inheritor of late friend Ted Kord's title and scarab, Batman has taken something of a guarded interest in the third Blue Beetle, though the nature of Ted's death and Batman's intimidating reputation has thus far prevented much contact with one another beyond the mission at hand.
Jason Todd - The second Robin. Jason's death scarred Batman permanently, and his subesquent ressurection and morally questionable antics has rendered them estranged.
Terry McGinnis - A Batman of the alternate future. Still relatively unfamiliar, but welcomed as part of the family.
Tim Drake - The third and (at least in Bruce's native time) current Robin. A natural adoptee to Batman's training, they have a seamless working relationship. Although Tim originates from before his adoption into the Wayne family, Bruce considers him as much a son as the other Robins.
Brainiac 5 - Relative strangers, though the Coluan's reputation preceeds him. Batman has already sought his help in an earlier case and approves of his pragmatic approach to superheroics.
Doctor McNinja - Something of a surprise. A deadly, capable admirer?
Leon Kennedy - Chief of Security and begrudging ally. Though they facilitate one another's work when required, neither approves of the other's methods. Leon thinks Bruce is crazy and Bruce fails to understand why that ought to be an issue. Both take great humour from undermining the other's authority.
Lex Luthor - Good with his grey matter, but on no accounts to be trusted. Bruce attempts to simultaneously keep a close eye and a fair distance from what has rapidly become one of his chief antagonists on the ship.
Motoko Kusanagi - Has the honour of being the first person to take a swing at Batman. It hurt. They work together well enough, but any discourse beyond shop talk tends to go horribly, horribly awry.
Rogue Squadron - There mostly for the training. The other pilots annoy him with their incessant desire to socialise. Why won't they leave him alone, Goddammit?
Everyone else - Disliked until proven otherwise.