Is it advisable to try to discover a place to make a ground connection on a board with a separate AC power supply?
More than likely, the voltage fed to the speaker is large enough to drive the photodiode in an opto- coupler. You can check this by using a standard low power LED and a resistor in series. You could also look at the signal across the speaker with your oscilloscope but there is a danger that the chassis of the doorbell receiver is "live". Best way to check this is with a multimeter on AC between local ground on your house wiring and one of the speaker terminals. If the chassis is live you'll certainly measure your local AC supply voltage and so don't use the o-scope.

Bottom line - be careful and wire the LED+resistor onto the speaker with power off.