'...that bit one': dubious hangover remedy (4,2,3,3)
I believe the answer is:
hair of the dog
(Other definitions for hair of the dog that I've seen before include "For example, setter's warmer" , "Maybe one in the morning" , "'...that bit one' completes a dubious hangover remedy" , "Alcohol as hangover cure (colloq.)" , "A morning-after drink?" .)