[broadgage]

A bell transformer often uses one or two watts, forever off load.
I measured over two watts a few years ago, I used a cheap plug in power and energy monitor.
These are not very accurate at low loads, but I had access to numerous bell transformers and measured the load of about a dozen connected together.

Just over 2 watts would be about 20,000 watt hours a year, or 20KWH. At 15 pence a unit that will cost about £3 a year.
A set of batteries will cost about that much, but last several years.

Battery operation has the merit of working in a power cut, not common in most places, but still an advantage.

The most economical system of all is probably a rechargeable battery that is already required for some other purpose and that can also supply the door bell at zero extra cost.
I have a home made 12 volt battery backed PSU that supplies various circuits including the door bells.
The losses are probably worse than a bell transformer, but the PSU was required in any case for other purposes and the extra losses from also working the door bell are zero.