Using a dual winding transformer to provide dual winding AC and DC of a single winding
This is more-or-less correct. If you put a capacitor on the output of the bridge it will charge to about \$12V\cdot\sqrt{2} - 1.4V\$ or about 15 or 16VDC. Any ripple will subtract from that.
Note that there is no common ground between the 24VAC and 12-16VDC.
Also, you are loading one side of the transformer more than the other so you won't get the full available VA out of it.