Bachelor parties (and other parties where a man is being celebrated, such as a birthday party) sometimes have featured a stripper who pops out of a cake. The origin of this seemingly American custom (popular in the 1950s, but faded since women’s movements of the 1970s) is unknown.
 
A classic cartoon in 1955 shows a chef pointing out that the girl goes in after you bake the cake!
 
“What happens at a bulimic bachelor party?”/“The cake jumps out of the girl” is a joke about the opposite of this cake jumping.
 
 
Wikipedia: Pop out cake
A pop out cake, popout cake, jump out cake, or surprise cake is a large object made to serve as a surprise for a celebratory occasion. Externally, such a construction appears to be an oversized cake, and sometimes actually is, at least in part. However, the construction is usually cardboard. The inside of the object has a space for someone, traditionally an attractive young woman, to crouch and hide until the moment of surprise, when she then stands up and comes out of the cake.
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The concept became notorious after Stanford White put on a dinner on May 20, 1895, that included a scantily-clad girl, Susie Johnson, emerging from a pie made from galvanized iron, accompanied by a recitation of “Sing a Song of Sixpence”. A few months later, the “Pie Girl” having disappeared, The World ran a lurid expose of the episode that emphasized the prominence of the guests, who included Nikola Tesla and Charles Dana Gibson, and the scandalous nature of White’s affairs
 
Newspapers.com
19 October 1895, San Francisco (CA) Call, pg. 7, col. 2:
“THE GIRL IN THE PIE”—SUSIE JONSON’S INTRODUCTION TO NEW YORK’S LUXURIOUS BOHEMIA.
—From the New York World.
     
5 January 1950, Oakland (CA) Tribune, “This Is the Story of Your Town” by Jack Burroughs, pg. 33, col. 2:
“Supreme Cheese Cake” sounds like some dish with the emphasis on the “some,” but such fleeting visions as I may have had of a Conover model popping up out of a cake has been quickly dissipated by the sobering reality.
 
March 1955, Culinary Review: The Chefs’ National Magazine, pg. 5, col. 3: 
(Two chefs are in the kitchen. A blonde bombshell is being put in a large pot—ed.)
“NO. NO. NO. ALPHONSE! SHE GOES IN AFTER YOU BAKE THE CAKE!”
 
9 January 1959, Bridgeport (CT) Post, “Mr. Abernathy” comic by Ralston Jones and Frank Ridgeway, pg. 31, col. 1:
“THAT WAS A FINE DINNER. ARE WE GOING TO HAVE ANY ENTERTAINMENT?”
“YES, WE’RE SUPPOSED TO HAVE A GIRL JUMP OUT OF A CAKE.”
(In the final panel a cake walks in, with the help of some new legs. “SORRY I’M LATE, BOYS. THE BAKERY TRUCK BROKE DOWN.”—ed.)
   
27 September 1965, Long Beach (CA) Independent, Television Log, pg. C8, col. 4:
Farmer’s Daughter, Inger Stevens, Paul Lynde. Tony plans a stag party for Glen, and starts interviewing pretty girls to pop out of the cake.
   
Google Books
Tony
By Patrick Dennis
New York, NY: Dutton
1966
Pg. 159:
Greer arrived last, so drunk he could barely stand. “What are you doing here?” he said to his hostess. “Going to come out of the cake and dance down the table?”
     
New York (NY) Times
The Evening Hours
By ANNE-MARIE SCHIRO
Published: October 2, 1981
AT some parties, the main attraction is the guests. At others it’s the setting. At still others, the quantity or quality of the beverages served. But at three parties this week, while all of those elements played a part, the star was definitely the food.
 
When the Waldorf-Astoria celebrated the 50th anniversary of its twin-towered building on Park Avenue, there were five groaning boards and endless streams of Champagne for the 1,000 guests. Each of the buffet tables, adorned with ice sculptures, was dedicated to popular foods served in one of the last five decades. The fare ranged from potted meatballs to pheasant.
 
But it was the 21-foot-high birthday cake that dominated the Grand Ballroom. The cake’s five layers were iced in gold and white and topped by a revolving facsimile of the hotel made of gold sugar crystals.
 
’‘They should have the Rockettes pop out of the cake,’’ said Donald Smith, one of the guests. ‘‘No, it should be Ginger Rogers,’’ remarked John V. Lindsay. No one jumped out of the cake. But Miss Rogers did make the ceremonial first cut along with Jean MacArthur, widow of Gen. Douglas MacArthur and a longtime Waldorf Towers resident, and Barron Hilton, chairman of Hilton Hotels Corporation, which owns the Waldorf.
     
Google Books
Jimmy Durante:
His Show Business Career, with an Annotated Filmography and Discography
By David Bakish
Published by McFarland, 1995
Pg. 198:
1968: For JD’s 75th birthday, friends give a big surprise party at Chasen’s in Hollywood, with seven-year-old CeCe popping out of the cake.
 
Google Books
11 March 1996, New York magazine, “His Kampf” by Jacob Weisberg, pg. 20, col. 1:
Last week Joan Rivers, stumping for her pal Steve Forbes in Arizona, piled on. She was at a party for Pat Buchanan, she told a radio interviewer in Phoenix. A Nazi jumped out of the cake. (The Forbes campaign later apologized to Buchanan.)
     
Google Books
On Sunset Boulevard:
The Life and Times of Billy Wilder
By Ed Sikov
New York, NY: Hyperion
1998
Pg. 423:
Sensing the ongoing tension on the set and hoping to dispel it, Curtis hired a real stripper to pop out of the cake during the filming of Spats’s birthday party.
(Actor Tony Curtis during the filming of Some Like It Hot, released in 1959—ed.)
   
Google Books
E-Plan Your Wedding:
How to Save Time and Money with Today’s Best Online Resources
By Crystal Melendez and Jason Melendez
Published by Mediasoft Press
2007
Pg. 420 (Bachelor/ette Bashes):
In fact, a traditional custom for the groom-to-be (just slightly less known than the stripper-jumping-out-of-the-cake routine) has long been to fill his and his groomsmen’s glasses and toast his new bride.