Simple past for the main verb 'have' implies completion. At the time of potential 'answering', the bath was 'had', i.e. finished, so the response is illogical-- if the bath were completed, then s/he could have answered the telephone.
('Was in the bath' of course makes it obvious that the person was immersed at the time of the phone call.)
Incidentally, 'was having' would work fine: 'because I was having a bath'. Now, using the continuous form, the time frame is clearly that the bath was in process when the phone rang.