The texture of the bow was not changed in the Texture Update, unlike many other items. This has resulted in it looking subtly but annoyingly different from the crossbow in terms of art style; despite being made of mostly the same materials the crossbow looks slightly redder and shinier than the bow does, and the string also has a slightly different colour.
I attached some bow textures I made
You can add them to a resource pack to experience the bow if it was changed