The rogues must be disappointed when Batman is out of town, fighting aliens and saving the world with his silly gang who wear their undergarments wrong.
The Riddler would just up and leave when Green Arrow shows up (per Batman's request since none of his kids were available at the moment). The archer would scratch the back of his head and give the wrong answer at least 38 times before the Riddler goes "yeah fuck this shit" and walks out, not bothering to actually blow up the hostages like he said he would - since it would've been unfair to those poor civilians, left to the mercy of a buffoon with a weird goatee (c'mon, seriously? Nygma had a spandex phase and even that wasn't as bad as this!)
Joker wouldn't even bother showing his face. Instead he would take a page out of the bat's book and brood in the darkness of his base, contemplating finding a way to send himself to space in order to see his beloved nemesis.
Ivy would go on a rampage because the Flash stomped all over the flowers she had planted in Gotham City Park. Batman was a man and a menace, sure, but at least he respected her creations and took care not to cause any damage to them when he's on patrol. He even found a lone lily growing between the cracks in the pavement on the sidewalk at some point, carefully put it in a pot and brought it to her. (it was very considerate, she even gave him a kiss - which didn't affect him negatively, thank you very much!)
Overall, the rogues gallery hate it when Batman isn't in Gotham. They especially hate his colleagues - how the bat can tolerate them is a mystery to them, especially regarding that Lantern guy (blegh).