The 7812 is a fixed voltage regulator… Check for variable regulator chips like the LM723. rigged with a 9 volt zener as reference it should give you the output you’ll need… For dropping 18 VAC to 9 volt DC your full wave bridge might be overkill. A full wave rectifier will provide DC at 1.4 x the rms AC input. Your raw DC will be around 25 volts and you’ll be dropping 16 volts to get your 9, a waste of power. Also 50 PIV diodes are quite adequate for use with these levels.