Bed sharing was a common practice up until the Victorian era. Partially this was practical, as homes were poorly insulated, and heating methods were crude by modern standards. If you look at existing examples of frontier homes from pre-Victorian eras, you see single room homes with central fireplaces, or a family sleeping room in an attic room, where heat would collect.

To the north of Fort Smith, where the movie is set, is a state park with several original farmsteads dating to the Civil War time period. (Prairie Grove Battlefield Historic State Park). Among those homes is a Dog-Trot style cabin (two separate rooms connected by a central porch. One room served as a kitchen, the other a family living quarters.) A larger log-style home, the Latta House, has a chimney on either end of the home a bedroom for the parents and a communal loft room for all the children.

Additionally, travel pre-industrial revolution made it so that it was common for visitors to stay overnight. You can see this in the practice of bundling, where a courting couple was allowed to sleep in the same bed as long as the gentleman was tied into a sack. The idea was that the couple could safely get to know one another and share things that they might not while under the supervision of a chaperone. However, this practice was common to the northwest. Oral tradition does not support this as a widespread practice in Arkansas.

Bed sharing was also a common practice when there were no extra beds to spare. In one famous example, John Adams writes in his diary that on September 9, 1777, he and Ben Franklin were obliged to share a bed at a crowded inn (and spent the night arguing over whether the window should be open or shut).

This all changed due to two factors. The industrial revolution made it easier to build warmer, more comfortable homes (with warmer, more comfortable beds).

Additionally, Victorian values shifted and privacy became a priority. Upper class couples in England had their own rooms, and separate rooms for each child. The idea of communal sleeping was seen as immoral and unhealthy due to impure body odor. The Victorians believed that bad odors (called miasmas) caused disease. All of these ideas filtered down to the middle and lower classes, who emulated the upper classes as much as their means allowed.

The other thing to consider is what the author was trying to accomplish. True Grit was a serialized novel appearing in The Saturday Evening Post. The author, Charles Portis was an Arkansas native. He wrote True Grit in 1964, and appears to have done extensive research before writing the novel. (The character of Rooster Cogburn, for example, is composite character of several Deputy U.S. Marshals serving under Judge Isaac C. Parker, including the deeds of Bass Reeves, and the appearance of Cal Whitson).

The theme that Portis is exploring in True Grit that is most relevant to our interests here is that of main character overcoming other’s perceptions of her. In the book, the main character is Mattie, a fourteen year old girl with a very Proper Christian outlook.

In the relevant passage in the book, she’s paid for a night’s lodging. The innkeeper pushes her in with an elderly lady. It would have been something that the old woman was comfortable with (due to it being more common in her own youth), but Mattie as a younger person might not have been as comfortable with it (due to the practice falling out of favor).

When Mattie looks hesitant, the innkeeper dismisses her reluctance as one would dismiss a child. Mattie is left with the bitter feeling that she’s been taken advantage of, due to her age and gender.

The author may also have been drawing on regional hierarchal family traditions. These traditions usually place the father in a place of privilege, followed by the mother, then any single or widowed female dependents (such as a spinster aunt or widowed grandmother) followed by older male children, then older female children, then younger children. These hierarchies persist in some rural Midwestern families to this day, and may be seen in traditions such as the male relatives eating first or taking the first bath. Under such traditions, it wouldn’t be unusual for a child to be pushed in to sleep in a room with a grandmother. It would also serve in the story to reinforce Mattie’s feeling of being treated like a child.

This is the first of many times people will underestimate or try to take advantage of Mattie due to her age and gender. The examples escalate as the book continues.

So the tl;dnr answer is that the practice was dying out, but it was a useful trope for the author to use.