Definitely weird about the bonded on badge and chrome come to that.
I've never seen a BSA chromed badge, but that that don't mean they don't exist.

The bars on a 1957 one are like these on another BSA.
These are plentiful and cheap, but may be later than your machine.
Me, I'd fit a pair them and then, if you find out the particular model you have, you can then fit the correct type.
The correct type will probably be like these Raleighs of the period:
http://www.sheldonbrown.com/retroral...and/index.html
The Sports Roadster types.

It's cool to have a bicycle twice your age.
Twice my age is Penny farthing territory