Running a bath in bedclothes for housemate (10)

I believe the answer is:

cohabitant

'housemate' is the definition.

'running a bath in bedclothes' is the wordplay.
I cannot really see how this works, but
'a' could be 'an' and 'an' is found within the answer.
This explanation may well be incorrect...

'for' acts as a link.

(Another definition for cohabitant that I've seen is " flatmate?".)

I've seen this clue in The Guardian.

Want a hint initially instead of a full solution? Install my app