One avoids bye by involving a couple (1,4)
I believe the answer is:
a deux
'involving a couple' is the definition.
(French phrase meaning involving two people)
'one avoids bye by' is the wordplay.
'one' becomes 'i' (Roman numeral).
'avoids' is a deletion indicator.
'bye' becomes 'adieu' ('adieu' can be a synonym of 'bye').
'by' becomes 'x' (multiplication sign**).
'adieu' with 'i' removed is 'adeu'.
'adeu'+'x'='A DEUX'
(Other definitions for a deux that I've seen before include "Intimate" , "involving two people" , "couple in Paris" , "together as a couple" .)