I saw a film in the 1960s that was made in the U.S.A. in the 1950s. It was a well made film in black & white on the lines of those that the BFI produce and was about a young white lady in the american mid west who was a struggling cocktail/bar pianist who managed to get a job in a local bar and she was good. They soon realised this, but that's about all I can recall. But she did play a beautiful version of 'Where or When' and 'My Ship'. I need to know the name of the film before I can try to purchase a copy of it.

Doesn't fit your timeline, but I thought I'd throw it out there anyway. Try Alice Doesn't Live Here Anymore. The piano Where or When scene starts around 1:20. YouTube (http://www.youtube.com/watch?v=5MyC5pk3yG0)