When Huntress and Gibson enter the bar, Gibson triggers a switch connected to a bust of Shakespeare, much like Bruce Wayne did in the original Batman (1966) TV series to enter the Batcave. In Batman, the button was concealed in the neck of the statue. In this episode it is triggered by turning the bust.
Morton says that he moved to New Gotham from Bludhaven. Bludhaven is the hunting ground for Nightwing, who as a teenager was known as Batman's sidekick Robin.