Batman brought his jet around under Superman's orders, not that he wouldn't have moved in to catch Robin before she fell anyways. Sure, he could have been the one giving the orders but it was good for team unity for the others to see Superman in a position of authority. He was something of a symbol after all, not just to the other heroes here but to the world at large. With that in mind, he should probably formally introduce Madison to the rest of the League members here ifs he hadn't introduced herself already once this was over. Her reaction would probably be an even more intense version of the sort of enthusiasm she applied to her work as Robin, which...could be interesting, he supposed.

To ensure that that meeting could properly take place he retracted the canopy again and swept low nearby the robot, slowing just enough that Madison could make the jump back into the cockpit safely and use the jetpack for insurance if she missed. He might trust her enough to scale a giant robot with some help, but it would be meaningless if she got too excited from the fact that she'd just helped destroy a giant robot, miscalculated the jump and had to be rescued from plummeting into the sea at terminal velocity.

Once the robot inevitably fell Batman would make sure to remember its' position in the water exactly and plot out where the ocean currents might have caused any stray pieces to drift or wash up. The right sort of carefully executed bribes and even more carefully executed legitimate paperwork by Bruce Wayne would ensure that the inevitable salvage or clean-up teams were blocked from delivering the robot or any of its' parts to Luthor. The last thing any of them needed was Lex weaponizing alien technology after the League practically disarmed and gift-wrapped it for him right off of Metropolis' shores. 

A little more careful paperwork and a few more bribes would ensure they instead delivered them to one of several high-security storage bunkers that just [i]happened[/i] to belong to a subsidiary of a subsidiary's subsidiary of Wayne Enterprises. Lex not being good enough to deserve extra-terrestrial toys didn't mean Batman shouldn't know the best ways to break them if more showed up.

But first he had to catch Madison. Then, even more dangerously, he'd have to survive her squeeing.