Bobby, best at heart, just gets by (5)
I believe the answer is:
copes
'gets by' is the definition.
('cope' can be a synonym of 'get by')
'bobby best at heart' is the wordplay.
'bobby' becomes 'cop' (I've seen this in other clues).
'at heart' says to take the centre.
The central letters of 'best' are 'es'.
'cop'+'es'='COPES'
'just' is the link.
(Other definitions for copes that I've seen before include "Manages successfully, gets by" , "Manages; church vestments" , "'Manages, gets by (5)'" , "Somehow manages" .)