Apart from when someone is out, the most obvious time to have an answering machine on is when when going to bed.
There is a strong chance of not hearing a phone when asleep. Or not waking and getting to the phone in time. So what better time to have the answering machine on ?
It is likely that the answering machine would be permanently on. For obvious reasons. People don't turn their fridge off when it's empty.
The problem Bamber has with the answering machine being on, is that it badly incriminates him. He said himself he was upstairs 'sleeping like a log'. So would not have got to the phone before Neville had left a message.