My first thought is that the letter shapes are too fine for wood. Really thin lines and serifs. I can't think of any easy way to ensure that the tiny gap where the B hooks over the bottom curve of the S would come out clear, or at least stay that way for very long.
One thing I have considered is to use a solution of sal ammoniac, aka ammonium chloride, and paint images with it. From what I've read, when a heat gun is used on the treated surface, the chemical decomposes, and leaves a hydrochloic acid on the wood, which burns in. Aside from finding no local source for the chemical, every picture I've seen from when it is used to do wood burning shows an image that is too blurry at the edges to make the logo you propose clear.
Sorry, not much help.