Oh, he hardly minded the dog's affection. It was nice, really, and though he'd had Martha back in Gotham cats weren't... quite the same. But Eddie was looking after her so far as he knew and it was probably better that way. Bruce felt like a different person, here, like he could shed his tired old persona and start piecing together who he was underneath. Gotham was Gotham, and this was this. He wasn't ready for the two to meet just yet. Maybe someday soon, yes, but not today.
Her surprise and confusion were impossible to miss, but he didn't let either deter him. He couldn't. Her attempt at Italian made him smile, perhaps a touch too fond before it evened out into something more appropriate; his life was a tangled web of a mess, and he didn't want to get her mixed up in it any more than necessary. A fine line to walk, maybe an impossible one, but his intentions were to try.
"Buongiorno," he echoed, making no actual attempt to correct her pronunciation. He hesitated, just for a moment, before extending a hand to her. "Walk with me?"