Bugs British character — and the rest — American sent back (8)
I believe the answer is:
bacteria
'bugs' is the definition.
(I've seen this before)
'british character and the rest american sent back' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'character' becomes 'air' (air can mean a character or mood).
'and the rest' becomes 'etc' (et cetera).
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'sent back' is a reversal indicator.
'air'+'etc'+'a'='airetca'
'airetca' reversed gives 'acteria'.
'b'+'acteria'='BACTERIA'
(Other definitions for bacteria that I've seen before include "source of disease" , "Cabaret I found containing microscopic organisms" , "could make you feel bad" , "Care a bit about these micro-organisims" , "Possible cause of disease" .)