Bucky is found to be sleeping on the floor in the pilot episode of The Falcon and The Winter Soldier. And the reason for this can be traced back to the 2014 film Captain America: The Winter Soldier. Bucky Barnes in this show is introduced by a way of flashback nightmare as an assassin, from which he is suddenly awakened in his bed, which would be a floor in this case. To understand Buck’s pathetic living condition we need to remind ourselves of an earlier scene shared by Steve Rogers and co-star Sam Wilson.
Bucky became what is known as The Winter Soldier, during his time on the Hydra Operative being one of the most secretive and effective assassins who has set foot on the planet. As of now after the operation, he is experiencing PTSD nightmares of his assassinations. One of these nightmares is that Bucky introduces Bucky in the new MCU spinoff show: He mistakenly kills both the target and the innocent in one of his missions in the Hydra operation, making him sweat profusely in his sleep and awakening on the floor post this he has confronted this to the therapist in the next scene. And the second Captain America film explains why he is comfortable with sleeping on the floor.
In Captain America: The Winter Soldier, Sam Wilson, and Steve Rogers meet after the latter runs laps around the former in picturesque Washington, D.C. The two of them later were found to be bonding over their shared military experience, Sam pointing out that the bed is very soft and marshmallow like making him uncomfortable to sleep. He feels that the bed is swallowing him while sleeping. Therefore the logical conclusion is that he must be sleeping on the floor because of this. Softness implies comfort in the minds of the military men, but Bucky has to constantly stay alert hence he cannot sleep in that soft sack as he is supposed to be alert all the time.
There were many instances when the MCU movies have introduced the mind grueling stuff like PTSD as Tony Stark struggled with it in Iron Man 3 and Captain America: Civil War. This sequence of Bucky struggling in his sleep on later as we witness him sleeping on the floor to the again the conversation while they were discussing the military experience is very subtle with no further exposition. This reminds the viewers of the gruesome and excruciatingly difficult stuff they face on a day-to-day basis. On a whole, this makes Bucky a severely damaged psyche and a troubled sleeper.
Bucky may not be completely healed from his past traumas but we can see future episodes of his experiences with Wakanda and with the Avengers following the demise of Alexander Pierce. It is still an enigma if Bucky manages to completely overcome his mental health struggles but we have a long way to go in The Falcon and The Winter Soldier series. Let’s hope he will!