Billy Rose nicknamed her “Jailbait” — but Paulette Harwood was too young to know what the great showman meant. After all, she was just 16 when she started dancing at his Diamond Horseshoe, in the basement of Times Square’s Paramount Hotel.

The glitzy nightclub was in its heyday in 1943 when Paulette arrived, fresh from ballet school.

And while the club fell on hard times — closing in 1951, its once-elegant interior trashed — it reopened Dec. 31, 2013, with a production called “Queen of the Night.”

Harwood, who might lay claim to that title as well, was there to see it.

She returned there the other day with 20 of her ballet students, who took the bus down from Newton Upper Falls, Mass., to see where their famous teacher once danced.

Now 87, her thick, honey-blond hair gone white, Harwood patted the stage, her eyes moist. “It brings back such wonderful memories of my grandmother,” she said of the woman who raised and chaperoned her. “I was just so happy to be paid, doing something I loved!”

Growing up in Brookline, Mass., the only child of parents who divorced before she turned 1, Harwood can’t remember a time she wasn’t dancing. At 14, she skipped school to audition for the Boston Opera’s “The Merry Widow.” She made it into the corps, spending her freshman year en pointe.

Her ballet teacher was Harriet Hoctor, a former Ziegfeld Follies girl and favorite Rose dancer and choreographer. But Hoctor was tired of performing, and knew whom she wanted to succeed her.

She personally took her star pupil down to the Diamond Horseshoe, where Rose saw Harwood dance and hired her on the spot.

Did he know she was 16? Harwood shrugs. “Billy knew it, but he didn’t know it,” she says. “I was supposed to say I was 18…but he was very good to me.”

He was protective, too, letting her and her grandmother, Dodo, stay in the hotel for free. Harwood commuted to work by elevator.

Her pay was $100 a week, a nice chunk of change back then, especially for a high-schooler. Besides, the club had a kitchen — “where the food was delicious, and I was so skinny, they kept trying to feed me!”

Even so, she got her share of unwanted attention. But Harwood was there to work, not play. “If [men] asked me out, I told them I had to take my grandmother,” she says. “They weren’t interested after that.”

Her show was a revue titled “The Post War Preview,” which forecast a world free of the fighting that dragged on for another year.

Rose, who by then had divorced Fanny Brice, the original funny lady, was a lyricist as well as an impresario, and supplied words to “The Blue Danube Waltz,” which a young man sang as Harwood pirouetted.

As soon as she finished, she ran upstairs to change for the big cancan number.

When she wasn’t dancing, she did her schoolwork, typing her papers on the pay machines in the hotel lobby. A dime got you 30 minutes of typing time, so she learned to type fast.

But even a high-school girl can be a teacher.

“The showgirls were beautiful, but they didn’t know how to walk,” she recalls of Rose’s “Long-Stemmed Roses,” who were all 6 feet or taller.

“They’d go clunk, clunk on their heels,” Harwood recalls. Like a mother duckling with very big chicks, she led them around until they’d achieved a modicum of grace.

They all towered over Rose, who barely cleared 5 feet. “He’d climb on a table and give directions,” she recalls. “Every time we turned around, he’d be on top of a table!”

After six months, Rose decided to take his revue on the road and entertain the troops. Harwood and her grandmother came along, and Rose took them to USO halls, bases and hospitals at his own expense.

She came home in time to graduate from high school, then returned to New York to dance at the Copacabana and the Latin Quarter, whose stage door opened onto Times Square.

On VJ Day, she and the other dancers spilled into the street, falling into the arms of sailors. “They were all kissing the girls that day,” she says, and yes, she was one of them.

In 1945, she joined Radio City Music Hall’s Corps de Ballet, not to be confused with the Rockettes.

“That’s a dirty word in our language,” she sniffs. “We could outdance the Rockettes any day of the week!”

The rival dancers had separate dressing rooms: the ballerinas on 50th Street, the Rockettes along 51st.

Three years in, she hurt her ankle so bad, she couldn’t dance. She returned to Boston, opened a ballet studio, met “a cocky little Irishman” on a blind date, and fell in love.

She and her husband, Paul, went on to have three daughters — all of them dancers, one of whom married actor Peter Gallagher.

All in all, she says, a good life. A dancer’s life.