well you have 2 things a door bell must do, once triggerd play a note or tone to alert the owner of the premisis, and after releasing the button or a short time following releasing it stop the tone,
in my own mind you have 2 options, either make it so when the button is pressed power the 555 and it should based on your values play its tone, and use some capacitance on the supply to keep it powered for say 1.5 seconds following a press, or 2, use a 556 and have the second 555 kill the first say 1-2 seconds after releasing the button,