Bug snug in this hairpiece? (3)
I believe the answer is:
rug
I believe this is a double definition.
'bug snug in this' is the first definition.
(as in 'snug as a bug in a rug')
'hairpiece?' is the second definition.
(rug is a kind of hairpiece)
(Other definitions for rug that I've seen before include "Thick floor-mat or coverlet" , "A bug may be snug in it" , "wrap" , "Wig (facetious)" , "grace the boards" .)