First off, let’s get one thing straight — so to speak. The title character of “Priscilla, Queen of the Desert,” now making its Long Island premiere at the Patchogue Theatre, fits none of the LGBTQ categories, unless B stands for bus. Although she — it — boasts a wardrobe replete with glittery get-ups, Priscilla is a bus whose mission is to transport two drag queens and an aging transgender woman from Sydney to the central Australian outback.

The soundtrack to their epic journey, played disco-live by Michael McAssey’s band, echoes the playlist of their nightclub career as Les Girls, singing and shimmying to 1970s-’90s jukebox hits. None were actually girls until Bernadette completed her transition. Tick, a hard-body partner in the trio (Mitzi on stage), brings Bernadette out of retirement to join an act that includes a rapacious young queen, Adam/Felicia, who thinks it’s as safe to flaunt it in the country as it is in the city.

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Tick, played in this spectacular Gateway production by Tony winner Jarrod Emick (Joe Hardy in the 1994 “Damn Yankees” revival), brings a veiled machismo to the role, appropriate for an avowedly gay man who secretly — to his partners — has a wife and son. That’s why he’s making the trek to remote Alice Springs: His wife books their show for her casino. Their 8-year-old has never met his dad.

Smartly directed by David Ruttura and framed by Stanley Meyer’s adaptive set, “Priscilla” never loses its sense of humor, even in darkness.

William Selby’s Bernadette sings like a diva in “I Will Survive” and presents an imposingly dignified woman who remembers how to fight like a man. She and Tick rescue “Felicia” (a dandy Matthew Marks) from rednecks who are shocked to find that she’s a he, following John Denver’s “Thank God I’m a Country Boy.” Bob (Mitch Poulos), a mechanic who fixes broken-down Priscilla, is a fan who nostalgically recalls Les Girls in “A Fine Romance.” His fascination with Bernadette becomes a revelation as Tick hilariously delivers “MacArthur Park” upon discovering the meaning of the lyric “Someone left the cake out in the rain.”

Wearing the original 2011 Tony-winning costumes by Tim Chappel and Lizzy Gardiner, a gyrating company of dancers, choreographed by Gerry McIntyre, reminds us — even in the face of gay-bashing and hate speech — that these girls “Just Wanna Have Fun.” We had fun, too.