The crafting book does not show the recipe for bamboo hanging signs until you have any stripped log in your inventory, even though stripped logs aren't used to craft bamboo hanging signs.
If the items bamboo planks and chains are in your inventory, you can craft the hanging sign but the recipe for crafting the hanging sign will not show in the crafting book.
The recipe unlocks when you have any stripped log in your inventory. Which seems unintuitive, still.