Time to cuddle up to current bedtime companion (5)
I believe the answer is:
teddy
'bedtime companion' is the definition.
(teddy bear)
'time to cuddle up to current' is the wordplay.
'time' becomes 't' (abbreviation).
'to cuddle up to' says to put letters next to each other.
'current' becomes 'eddy' (eddy is a kind of current).
't'+'eddy'='TEDDY'
(Other definitions for teddy that I've seen before include "Child's soft toy" , "Bear - boy" , "plaything" , "A child's toy bear" , "Cuddly toy" .)