I really don’t like “Mrs. A.J. Wilder” because the suffragette within me opines that she isn’t treated like a person in her own right by using her husbands initials instead of her own first name.

I hope not to offend anybody but when I read her nickname Bess or Bessie I think of a cow in the first place because when I was a child we had a reddish-brown cow called Bessie.

It’s not a dogma but usually I refer to her this way:
I use “Laura” when I write about the literary character in her books.
When I write about the real woman, especially the author, I name her “Laura Ingalls Wilder”, often shortened LIW.
(Fast spoken in German, the initials are pronounced as a single word, which sounds like “Ellie-We”. That’s why I like the abbreviation so much.)