Keeping in mind that this forum exists so that the uninformed may provide the least appropriate, most complicated, least reliable solutions for established problems with established (and reliable) solutions such that the requester of such information may be relieved of taking responsibility to do the right thing in the first place, over-complication is the natural order of things (Thank you, TImothy).

https://www.radioshack.com/products/...nt=20332219525

Put it in a small WireMold box right inside the door by the door jamb. Feed it from the bell wire - take one lead, and connect the buzzer in SERIES with that lead. At 58 ma, it will not overload your transformer.

Peter Wieck
Melrose Park, PA