When he sees her and she introduces herself as Bela Talbot, he doesn't question the resemblance—after all, there's Elena Gilbert and Katherine Pierce in his life and they're identical so he figures what the hell.
One hour later he notices that she's human and for a brief second he wonders if he's got some thing for human doppelgangers. A couple shots of whiskey fixes that, though, and she challenges him to see who can drink more.
He laughs. "I can drink you under the table," he says but she takes that as a challenge.
Four hours later and he is maybe starting to feel a buzz.
He remembers that this woman who looks like Rose—Bela is her name—is human and declares her the winner even though he knows the opposite is true. She laughs loudly and gives him a kiss on the cheek. "I told you I could win," she whispers in his ear.
He calls her a cab then and he doesn't know if it's because she is way past her limit or if he knows being around her is unsafe for her and he doesn't want to hurt her like he hurt Rose.
Six hours later and he's finally reached an appropriate level of drunkenness for this occasion and with Elena and Stefan's help, he gets back to the boarding house without incident.
He falls to sleep with dreams of Rose and this woman named Bela playing in his head.