The phrase "at the edge of the bed" is correct and usable in written English.
It can be used to describe a location or position relative to a bed, often indicating where someone is sitting or lying.
Example: "She sat at the edge of the bed, contemplating her next move."
Alternatives: "on the border of the bed" or "by the side of the bed."
"You are honest and good," Ivetta had finally declared from her desolation at the edge of the bed.
On Saturday afternoon, Mr. Lundgard sat at the edge of the bed next to Emilie Gossiaux at the hospital on 17th Street.
There are all kinds of bedtime stories, those that lull you to sleep and those that keep you anxiously perched at the edge of the bed.
Mr. Campos snores, snorts, sounds like a drowning man, and, careful not to wake him, Mrs. Campos pokes and nudges him until he rolls off his back, now grinding his teeth but facing away, at the edge of the bed.
"It will leave audiences feeling like they are sitting right there at the edge of the bed," Stephen Shiu Jnr, who wrote and produced the £2m Cantonese-language film, told Chinese media.
Some nights, instead of staying hunched over his small wooden desk in the hours after dinner, muttering at the bills as he passed a slender hand over his smooth pate, he would stand up with a sigh and walk across the narrow hallway, into my room, and then, after doing a "super-duper tucker-inner," sit at the edge of the bed he had built and read "Winnie-the-Pooh" aloud to me.
If you do not have a frame, place your bed in a corner, but at an angle, so that the edge of the bed is parallel with the corner.
"I have this image of myself in my first rental apartment, sitting on the edge of the bed and staring at the window.
Bin Laden's wife Amal was on the edge of the bed shouting in Arabic at the SEALs, and Osama bin Laden dived across the bed, shoving Amal at the same time, for an AKS-74U kept by the headboard.
Bend forward at the waist, walking your fingers forward until you can just barely grasp the edge of the bed with your finger tips.
