If you want to see what towns or townlands are in a given registration area use this site below. (Search under Poor Law Union as the boundaries for most PLUs are also the civil registration district boundaries).
http://www.thecore.com/seanruad/
Parishes have different boundaries and can often be split across several registration districts.
Your question is where would a registration in Banbridge be registered. The answer is Banbridge. Dromore isn’t a civil registration town, it’s a parish and a small town. Some townlands in Dromore have Banbridge as their civil registration district. Others have Lisburn. The seanruad site above tells you precisely which.