The 3 - 32 VDC is the input side of the SSR. For a 12 volt system the output side would need to be DC rated as well not AC rated output otherwise it will not work.
To get your light bars and whatever else to flicker and strobe with the music you do not need to use a bridge rectifier for the input.
Just connect it directly to the amps output through the 10K potentiometer. It will feed half wave AC to the input with will give your lights a much stronger flickering and strobing effect as well.