The incredulous look L.L. had given him was exactly why Bucky didn't frequent the places he had like this unless he absolutely needed to for an assignment or to lure out targets. But this was one of the few that no one knew he had. Natasha probably knew of it, but she had never stepped foot over the threshold. And he knew for fact that Steve was probably clueless about this place's existence. To anyone looking, the apartment itself was owned by some distant relative of one James Barnes who was a bit of a recluse given how much he looked like his allegedly long dead relative.
"I don't live here very often," he clarified. He shrugged out of his coat and hung it up. "But if I'm wanting something that feels like home more than a safe house and I'm able, I'll come here. I mean, I do have some nicer safe houses scattered around the world but, this is the one that's closest to home for me." His eyes fell to a very old picture that sat on the mantle over the fireplace. Closer inspection would reveal that a very young Bucky, probably no more than eight or nine, was in the picture with a girl of a similar age and a couple who shared features of the two.
Tugging the fake skin of his left arm off, he placed it in a case before he headed to the kitchen to start cooking. "Feel free to explore. There's a T.V. in the living room." Gathering what he needed, he set to work on making one of L.L.'s favorite meals (which he might have done some snooping to learn).