Bill's oddly deep bath (4)
I believe the answer is:
debt
'bill's' is the definition.
(thesaurus)
'oddly deep bath' is the wordplay.
'oddly' indicates alternate letters (letters in odd-numbered positions).
'deep'+'bath'='deepbath'
The alternating letters of 'deepbath' are 'DEBT'.
(Other definitions for debt that I've seen before include "sense of gratitude" , "Intertwine" , "What's due" , "Amount owing" , "Money owed or due" .)