This is Barbara Dana, as seen in "Captive Audience", an episode of 'The Alfred Hitchcock Hour'. She is listed as "Folk Singer" in the IMDb credits (only by name in the show's credits.)
The episode took place in San Francisco and her scene was in a small, hip club.
Ms. Dana only has two acting credits on her resume, both of them in 1962 episodes of TV series. Her other role was in the series finale of 'Checkmate'.
That took place in San Francisco... And she played a gospel singer. No name given.
I think we all know where I'm going with this. But I'll also add that I think she was playing the televersion of herself in both shows. And she easily crossed genres with her singing career.