American in bed cover (4)
I believe the answer is:
coat
'cover' is the definition.
(I know that coat is a more specific form of the action cover)
'american in bed' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'in' is an insertion indicator.
'bed' becomes 'cot' (cot is a type of bed).
'a' inserted within 'cot' is 'COAT'.
(Other definitions for coat that I've seen before include "blanket" , "Outer covering" , "Jacket" , "Fleece" , "Apply layer" .)