That will probably work. But before you start, do you have any idea of what shape the enlarged hole is? Is it circular or a bit oval? Where exactly do you want the bush to end up, relative to the rest of the wheel?
It would be disappointing to get a firmly fixed bush if it made the wheel eccentric and wobbly.
Assuming that the gap you need to fill is quite small, this is what I would try.
Arrange three pieces of wire down the hole in the plastic so that they hold the bush straight and central. Looking at it in plan, put one at 12 o'clock, one at 4 and one at 8. With the right size wire, you could get a tight fit, sufficient to remount the wheel on the saw. You can then rotate it against a fixed marker to see if it is straight and flat. This stage may need some fiddling with different or extra bits of wire.
When it is all straight and central, force epoxy down the three gaps, leaving the wires in place. (Before you start, thoroughly clean and degrease everything.)
Good luck!