Batman refused Leon's invitation to take him somewhere safe from the reboot without any hesitation.
He saw no need to escape the reboot only to meet another Bruce Wayne in the post-reboot world.
They were both Batman. Their experiences were the same.
Changing worlds would not give him another pair of living parents.
Although Leon said that in some timelines, Bruce had died while the Waynes had survived.
After a brief hesitation, Bruce still chose to refuse.
"All right, then. Staying behind as someone who knows the truth and guards the grave of the world's past isn't bad either."
Leon pointed at Batman's liquor cabinet. "By the way, a fearless moment like this calls for high-proof liquor."
"For example, distilled vodka, known as the water of life. Ninety-six percent alcohol will set your boldness ablaze from your toes to the top of your head."
Batman silently glanced at his liquor cabinet. "Not a bad suggestion. I'll put on Tchaikovsky's Sixth Symphony to drink to."
Leon raised an eyebrow. "Now that's truly tragic. Goodbye, Bruce."
"Goodbye, Leon."
After leaving Wayne Manor.
Leon found Barry Allen in a residential house in Central City.
"Barry, you rebooted the world again. Did you know that?"
"What? Me? Why would I reboot the world?" Barry looked utterly bewildered. He was eating pasta he had made with his mother.
"You'll have to ask yourself that. The one who rebooted the world was you from the future."
As Leon spoke, he discreetly took a drop of Barry's blood and sent it into the Inner World for the Blacklight Clone to swallow.
Barry noticed nothing. He merely shoved the table aside in a panic and stood up.
"You're saying that I—future me—came to the present or the past and changed the world? Why!?"
He was living happily