Hello.
This is just my opinion. but I think your JB mark was used by Jonathan Bell of Sheffield England.
The first scan below shows his sterling mark entered at Sheffield in October of 1854.
Second scan shows the firms electroplate mark after they became " & Son" sometime later..
Have seen on the internet your mark attributed to Thomas Bradbury.& Sons. I don't think this is correct.
In the scans below we see Bradbury entering a sterling mark at Sheffield in May of 1889.
The shield is not the same and it was only used for a few years.
Pat.