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Are you sure your bridge is connected like that? If it is, D6 is toast.
The gain of the opamp is 1+ (R11/R10) so all you did was turn the gain way down.
The input must connect to the microphone with shielded audio cable to prevent mains hum pickup. The opamp circuit must be wired compactly and maybe in a metal box connected to 0V. It will probably pickup hum if the circuit is made on a breadboard.
Having a bridge rectifier in a package does not prevent one from connecting it incorrectly. If it is connected the way you drew it, you will have a half wave rectifier (and possibly a burned out diode), which could be the source of your hum.
Is the transformer rated at 18V RMS?
Are you able to measure the DC voltage at the input to the regulator?
Do you have an oscilloscope?
If so, observe the input and the output of the regulator, and tell us, or post a picture, of what you see.
What circuit are you powering with the regulator other than the modulator, and possibly a preamp? Are you also powering the power amplifier?