IMDB.com is the equivalent database for silent and sound pictures - and performers, etc.
According to the mini-bio (of unknown validity), Bebe Daniels (born Bebe Virginia Daniels 14Jan1901) is listed in this database as sister to actor Richard Daniels.

From personal experience, in the early days of stage and screen (before permanent stage names were adopted by the unions), there may appear many performers who share the same stage name (which was also misspelled by the press or mistranscribed in databases as you found out). Also the "studio system" of the 1930s fabricated new names and often new biographies for stars.

So the Bebe Daniels in IMDB could be someone totally different from yours, or the contributed bio (usually from reference books) is wrong or incomplete.

BTW, did the sheet music name the performance from which the song appeared?

Also check out Google Books - you never know if a mention may appear about either a performer, a play, or a song.
(Estelle McMeal/McNeal does not appear in GoogleBooks.)

I see you also posted 28 Jul 2006 on an Ancestry board that you think a "Elizabeth Estelle Anderson (1881-1968)", who married a doctor "Robert John McNeill Sr. (1874-1937)", may have also worked as an actress using "Estelle McMeal". (Is this the same person you are seeking in this message board?)

I share your frustation. I spent parts of 10 years searching for my grandmother's first cousin who was an actress on stage 1908-1921 and in silents 1915-1921, but little known today. (I was lucky I found her in several resources, including the NYPL.) I kept stumbling across a second actress who shared the same name, but who performed as a repertory actress 1881-1910, and it took a concerted effort to separate their career credits (and newspaper clippings).

I wish you the best of luck.