Hi Ross,
Unbolting the bumper is quite simple.
There is a small bolt holding the bumper to each side panel - this doesn't hold much weight.
And there are some big bolts holding the bumper brackets to the chassis rails at the front.
You can see these from inside the engine bay (from above or from below), two on each rail, just behind the radiator.
under the small side bolts and the bog chassis rail, then slide the whole bumper forward.
It is not practical to put in the 70's style smiley bumpers.
It's not even practical to put in the 1977-1979 chrome bumpers on your 1981 model.
A straight replacement from a 1980-1981 Celica is called for.
You might find a spare from the guys at
http://autos.groups.yahoo.com/group/classic-celica/
- Stepho