Make me a logo -- 2

We are a tiny business who make functional, personalized wooden gifts from reclaimed wood. We rescue the wood from all over our city and bring it back to our little wood shop and then give it new life. We build the pieces (eg. coasters, hook boards, bird houses, fridge magnets, greeting cards, custom signs) and then use professional grade wood burning pens to burn designs and messages into the pieces to create completely unique and personalized gifts. We currently only have an Etsy shop, but would like to offer our products to the local stores in our community, so we need a logo that we can use on our invoices and business cards. I am providing an image of something I quickly burnt into the wood to give an idea of what we would like, but I made it quite large and I would like a more simplistic version of this. I like the curly font, but think there must be a better way of making the 'WB' look like part of the wood grain. Our business is called The Wooden Badger (hence the 'WB') and we like to make our pieces look as natural as possible. We use reclaimed wood and recycled materials to produce our pieces, so we want the logo to be in keeping with the natural, simple, hand drawn look that our pieces have. Thank you!