That will give you the positive rail for 12V, minus the diode drop, so around 11V DC
But yeah, you can get the 24 VAC out of a transformer like that directly out of the secondary.
Something like this might do.
C1, C2 & C3 should be around 200V caps.
The transformer is a 120VAC to 48VAC, but this will be very crude.
You end up with a positive around 11V rail and a negative one.
Before the rectifier you have 24VAC, On the output of any of the secondary terminals respect to ground.
Edit: Forget R1 the simulation just needs a resistor to work.
Edit2: also on the transformer I used 25uH and 4uH to denote the 5:2 winding (squared Henrys) so it's just the ratio for a 5:2 transformer or a 120V to 48V AC transformer.