Yes, the Mini Rainbow Bridge consists of pine pieces. We do not offer a Balsa Wood Bridge at this time. The Balsa Rainbow is similar, but we understand it's not fastened as a "bridge".
An option for you might be to visit our sister site www.MakeYourOwnBirdToys.com. There you can find components such as Balsa pieces, beads, cordage and hardware if you'd like to make a bridge for your bird.
Thank you for writing, please let us know if you have any further questions. :)