My mother is a teacher with three masters degrees and she, too, insists on the veracity of this "fact." (Furthermore she insists that the plug in question is called a "Tappan" and resultingly the Tappan Zee Bridge never fails to make her smile.)

It's not that "they make a plug," but rather that a plug forms from the material that sloughs off from their digestive tract, bits of plant and hair that they groom from their fur in their sleep.

A quick google search of "bear hibernation plug" will yield more information.