Here's an exciting find. The below is from the December 15, 1892 Brooklyn Daily Eagle reporting on a reception of the Coronet Yacht club at Tivoli Hall in Brooklyn. Among the entertainers that evening we see "Miss Bessie Raymond, soprano soloist."
I'm betting this is Bess a full two years before she became Mrs. Houdini. "Bessie Raymond" was the stage name she used for her solo singing act before and after her marriage. She was a Brooklyn resident and she was a Miss! In fact, she'd be only 16-years-old here.
Until this, the earliest mention we have of Bess as a performer (or Bess in general) is the June 22, 1894 "Risey in the Box" article from the New York Clipper which mentions her as a member of the "Floral Sisters, neat song and dance artistes." (Try as I might, I've never been able to find any mention of the act elsewhere.) But Bess' sister Marie talks about Bess performing as "Bessie Raymond" before this, and I think that's exactly what we have here.
UPDATE: Just for clarity, the photo at the top of this post is not Bess in 1892. It's just the earliest picture of her I can find and is likely 1894.