You haven't mentioned any filter (like a capacitor) for the output from your rectifier. Without that, you will get full-wave DC, which varies every 1/120 of a second between 0 volts and the peak of your AC waveform, which itself is 1.4 times the RMS voltage. So, when you put 20 volts AC into the rectifier, the rectifier puts out an instantaneous voltage of about 28 volts, far higher than the 12 volts that the circuit was designed for. You will be lucky if it has survived.
It was also probably designed with the assumption that it would receive a reasonably smooth and constant DC supply voltage, not the wildly fluctuating voltage that you may be giving it. You can remedy this by putting a suitable capacitor across the output terminals of the rectifier. To know how much capacitance you need, you need to know how much current the circuit draws. For a peak-to-peak ripple of about .8 volts, you will need about 10 microfarads per milliampere. More capacitance is better.
With the capacitor in place, to get the desired 12 volts DC out, you should set the AC voltage into the rectifier to about 9 volts.
