There is no "simple" circuit that does the reverse conversion of what a full wave bridge does on a sine wave.
However, it is possible to get there from here. Most of what you are asking about is an inverter. That's the reverse of a DC power supply. You put DC in, and AC power comes out.
Put a big enough capacitor on the output of the full wave bridge, you have DC with some ripple. That can be fed into an inverter to generate the same AC power as is going into the full wave bridge.
Note that not all inverters produce sine waves. You would specifically need a "true sine" output inverter. Square wave and "modified sine" used to be more common. Nowadays the extra electronics to create a sine wave isn't that much more expensive, and it's usually better for the load. True sine inverters are common now.