Hi Karen,
First, the records office didn't have any electoral rolls between 1890 and 1947!
I was directed to the central library, which is currently housed in a load of portakabins while a new home is built as part of massive city centre development, and had my doubts whether half their records would be available. But yes, the rolls were there ... and ...
There's no sign of 30A Cowbridge Road. But - No 30 is home to a William Treseder, whose family ran a nursery (plants not kids) on the site until comparatively recently. And it's next door to the City Lodge.
So either your mother was born in one of Treseder's greenhouses or she may well have been in the Lodge, with, as you suggested, the 30A used to disguise the fact. A look at the 1940 Ordnance Survey map shows that the main building of the complex was marked as a hospital, so it may be they took patients (maternity patients anyway) from outside.
I'll ask around to see if anyone knows. Also, as the City Lodge was run by the council, there should be records of admissions and so forth at the record office, so if you like I'll ask next time I'm in there. (You'll have to give me her name and her parents' names if you want me to do that. PM me if you don't want them out for public consumption.)
Regards, Gareth