How to join these three pieces?

I need to join a 2 yards long dowel to another piece using the wooden bead stick - please see the picture. The dowel in the pic is just a remnant I used for taking the pic - the dowel I need to join is 2 yards long. And the top piece is about the same length as the dowel. The bead stick in the middle is already drilled through. How can I join these so it doesn't show hardware ? The dowel will be holding a very light piece of fabric. Thank you!