Resort to guessing just a little bit (10)
I believe the answer is:
suggestion
'just a little bit' is the definition.
'resort to guessing' is the wordplay.
'resort' is an anagram indicator.
'to'+'guessing'='toguessing'
'toguessing' is an anagram of 'SUGGESTION'.
(Other definitions for suggestion that I've seen before include "one may be going to box?" , "Idea put forward for consideration" , "suspicion" , "Proposition" , "Hint" .)