In 2268, Watley transferred from the Lexington to the Enterprise, where she encountered the temporally-displaced Doctor Julian Bashir and Chief Miles O'Brien, who were posing as Enterprise crewmembers while attempting to apprehend the Klingon criminal Arne Darvin. Meeting the pair in a turbolift, Watley flirted with Bashir, with whom she shared a mutual attraction, even informing him of the time of her scheduled physical.
When Bashir learned of Watley's name, he began to suspect that he was experiencing a predestination paradox, in that his great-grandmother's name was Watley, and nobody had ever met his great-grandfather. Informing O'Brien of his suspicion that he was destined to fall in love with Watley and become his own ancestor, Bashir was rebuffed by O'Brien, who felt that he was simply attempting to justify his attraction to her. Bashir's suspicions turned out to be unfounded, however, in that his failure to pursue a relationship with Watley resulted in no known alterations to the timeline, much less his non-existence. (DS9: "Trials and Tribble-ations")