The deceased could not have done so, as, according to the doctor, the poor lady must have died immediately.

Again, the assassin would not have been so foolish as to ring and thus draw attention to his crime, letting alone the question that he could not have escaped at that late hour.

We can only offer this solution.
"The assassin must have been concealed in the bedroom, and after Susan ascended the stairs to let Mr.Clancy out, he must have stolen into the sitting-room and have killed the old lady before she could even rise.
She might have touched the bell, and the button (the bell is an electric one) may have got fixed.

Later on, the heat of the room, warping the wood round the ivory button, may have caused it to slip out, and thus the bell would have rung.

Of course our readers may say that when pressed down the bell would have rung continuously, but an examination has revealed that the wires were out of order.