Can I give DC 12V to a AC 12V input?
If you have a bridge rectifier and want to feed 12VDC into it, there are a few things to consider.

In 12VAC, peak voltage would be about 17V, so whatever is after the rectifier (say a linear regulator possibly) its expecting 17V (minus diodes drop). If it is for example, a typical 7812 12V regulator, it needs at least 14V to work properly. If its a lower voltage regulator (say, unlikely 9V or 5V) it might work fine.

With AC, current flows through 4 diodes, feeding DC only uses 2. So they have to handle double the current (which may or may not be fine).

I wouldnt really recommend doing it this way. If it has a rectifier it probably uses DC somewhere down the line, and if you have a bench supply you can feed it there.

p.s.: you might want to take the precaution of disconnecting unused parts of the circuit, some regulators dont like to have voltage on their output higher than input and your circuit might not have protection for this.

p.p.s.: clarified in the comments but written here for future reference: a full bridge rectifier can give positive and negative power rails, which 12VDC do not supply.