Club that chap joined to go swimming (5)
I believe the answer is:
Here is my best explanation:
'go swimming' is the definition.
(I've seen this before)
'club that chap joined' is the wordplay.
'club' becomes 'bat' (I've seen this before).
'that chap' becomes 'he' (**).
'joined' means one lot of letters go next to another.
'to' acts as a link.
(Other definitions for bathe that I've seen before include "Swim for pleasure, and clean oneself", "Swim in sea", "Wash, soak", "Clean", "Take a swim; envelop", "Swim or dip", "Swim or paddle", "Wash; swim", "Become immersed in" and "Immerse in liquid for wash".)