Of U.S. origin, the phrase bottle episode, also bottle show, denotes a television series episode produced using a minimal number of sets, actors, effects, etc., often with a single location and only the main cast members. Bottle episodes are often intended to be produced inexpensively so that the budget for the series may be directed to other episodes with higher production costs.

In this phrase, bottle may refer to the constrained nature of such episodes—cf. below the quotation from the Chicago Daily News, and cf. to bottle up, meaning to confine, to contain. However, s.v. bottle episode, Merriam-Webster mentions that the phrase may refer to pulling a genie out of a bottle:

The notion that the phrase grew out of the television series Star Trek is contravened by Robert H. Justman, a coproducer of the original Star Trek. In discussing the alternation of “planet shows” with “ship shows” on the series, Justman mentions that “most other series called them [ship shows] ‘bottle shows,’ but regardless of what they were called, their purpose was the same: to save money by ‘bottling up’ the action … Our ship shows took place entirely on board the Enterprise and cost much less to produce” (Herbert F. Solow and Robert H. Justman, Inside Star Trek: the Real Story, Pocket Books, 1996, p. 253). In The Outer Limits: The Official Companion (New York: Ace Science Fiction Books, 1986) the book’s authors David J. Schow and Jeffrey Frentzen attribute the coinage of bottle show to Leslie Stevens, producer of the series The Outer Limits (1963-65): “No one believed Leslie Stevens when he proposed to complete an Outer Limits episode in four days … until he went ahead and did it. The skeleton of ‘Controlled Experiment’ [broadcast 13 January 1964] was typed up by Stevens on a New York to LA flight, and the show took four and a half shooting days to complete. At $100,000, it was the cheapest Outer Limits ever. Stevens dubbed this last-minute lifesaving technique the ‘bottle show’—as in pulling an episode right out of a bottle like a genie. ‘When they know you can do it, and do it fast, you become the fire department, to bail the show out of trouble,’ said Stevens” (p. 86). (Schow and Frentzen interviewed Leslie Stevens expressly for the book.)

The earliest occurrence of bottle show that I have found is from It’s Destination Failure for CBS’ Spencer’s Pilots, by John Camper, published in the Chicago Daily News (Chicago, Illinois, USA) of Tuesday 22^nd June 1976—the U.S. actor, director and producer Bob Sweeney (1918-1992) was the executive producer of Spencer’s Pilots, an adventure series broadcast on CBS from Friday 17^th September to Friday 19^th November 1976:

Sweeney will use some old Hollywood tricks to try to make his show succeed. He will overbudget the first few shows to try to attract audiences with a lot of expensive stunt flying and spectacular airplane crashes.
“You’ve got to stack the deck by putting the juice up front,” he said.
Then, in the highly unlikely event that the series lasts more than a few episodes, he will tell his writers, “Write me a couple of bottle shows.” A bottle show is one that is kept within tight financial limits (i.e., in a bottle). Well, I don’t understand the term, either.

The earliest occurrence of bottle episode that I have found is from Making Fake Flakes Isn’t So Easy for TV: For Believable Snow Job, A Mashed-Potato Fight, by Emily Nelson, published in The Wall Street Journal (New York City, New York, USA) of Monday 6^th January 2003—as reprinted in the Ottawa Citizen (Ottawa, Ontario, Canada) of Monday 27^th January 2003:

Snow, it turns out, is a big production worry for TV studios these days. […]
[…]
Sometimes TV shows in colder climates manage to write snow out of the script to avoid finding or making it, as when writers for Everwood, a new TV drama set in Colorado, added an unusually warm breeze that the town celebrates with a festival in one episode. They reversed the weather in two other episodes, writing in a blizzard that keeps everyone housebound and keeps the cameras inside. A show where the cast never gets outside is called “a bottle episode.”

A transferred use of the phrase bottle episode occurs—with reference to self-quarantining in order to prevent the transmission of Covid-19—in the last sentence of this extract from Family feuds: Single setting, limited cast, life as a suffocatingly raw TV episode, by Melissa Hank, published in the National Post (Toronto, Ontario, Canada) of Wednesday 15^th April 2020:

There’s a term that television bigwigs and smarty-pants like to toss around when discussing the intricacies of crafting a show: Bottle episode.
As in, an episode that uses just one setting and a limited number of actors for the duration. […]
One of the most famous—and most polarizing—is the season 6 Mad About you episode The Conversation, which sees married couple Paul (Paul Reiser), and Jamie (Helen Hunt), have a 20-minute conversation in front of their bedroom door listening to their baby cry herself to sleep.
It’s filmed in one take without a commercial break—relentless, suffocating and raw. Come to think of it, while we’re stuck at home and surrounded with just our housemates, many self-quarantining folk are living in their own version of a bottle episode, with varying success.