Holmes realized that
"....whatever danger threatened an occupant of the room could not come either from the window or the door" (pg 20)
Therefore, the furnishings in the room had to aid in the murder of Miss Stoner's sister. Sherlock's first hint is that the bell pull wasn't attached to anything. It didn't ring! It was a relatively new addition to the room, but Miss Stoner said that her sister never used it. When Sherlock investigated, it wasn't attached to anything but a hook just below the opening in the ventilator.
Secondly, the ventilator in the room opened into another room instead of opening to the outside for air. Sherlock muses,
"....what fool a builder must be to open a ventilator into another room, when, with the same trouble, he might have communicated with the outside air!"
The ventilator was added to the room about the same time as the bell rope.
Finally, the bed was clamped to the floor so that it would not move.
Sherlock deduces that the bell pull must be a bridge between something that passed through the ventilator to the bed. Since Dr. Roylett received a number of dangerous creatures from India, Holmes knew that he could find an animal that the Western world was not familiar with and that could kill with a deadly undetected poison.