I found the document (settlement of distribution of Mary Hill's Estate) with a signature of Burnie. Here it is
Here is the signature of the photo up for auction.
Liz is absolutely right, no resemblance between the Bs in Burnie's signature and the Bs in the signature in the photo for auction. So the signature in the photo is not Burnie's. Good hypothesis, Sue, but the evidence does not support it.
Here are some signatures of Bix.
A few more in the posting