I don't think Nolanverse Batman really can continue. The end of the Wayne corporation ensured that. There's no more money to be had, and worse, no more gadgetry/tech. Bruce can't do it anyway, he's broken. He is done. Oh, sure there's some way to write a magic saving throw on all that, but really. All the assets were liquidated or distributed or taken over, except the batcave.
Nightwing would be the next best thing, with JGL doing it, but that would be him just using whatever's leftover in the batcave. It could work, but...
It is my opinion that the Nolanverse Batman is over and done, except for the below:
1) As far as a JLA Batman, there's no real way to include BatBale, as the way that story was told... he'd have to be somewhere between Begins and TDK. I don't think that's a real doable thing, but there is your out to get him in it. It would be a one shot deal.
2) It's *possible* they could write some weird goofy story where Superman gathers all the stuff from the batcave and hides it, with Nightwing's help, and then kidnapps Bruce (and Selena?) to get him to help, dammit. Or something of that nature. Who else could do it? J'onn J'onzz maybe... but unlikely.
That second is going to highly be dependent on Man of Steel's story and how it ends, I would say.
I, for one, would be highly put out if JLA had Bale in it, or referenced Nolanverse at all. To be honest, as silly as it sounds, I'd rather they either just didn't explain how Bats got there, he just is. We all know his story. Or, and this would be killing it for sure, but they could reference Burtonverse Batman. And put nipples on the suit again. Heh.
They simply screwed up. They needed to get JLA done BEFORE TDK. After wasn't gonna work. Between Begins and TDK, they had the chance.
Now, they'll truly have to reboot it again, ala Spiderman, and do like the Avengers, to make the story work. Or have Joss Whedon come in and make the story work somehow, but even he would have a hard time. Maybe Kevin Smith, but I kinda doubt they'd even wanna work with him these days. Something about giant spiders...
Of course, all that's my opinion. We'll see what happens, won't we?