Mulberry and osage are close cousins. Mulberry is even yellow and changes color with age just like osage. There are two types of mulberry, red, and white. I have built bows if the red but not if white. Just make the bow a little bit wider thicker longer than osage and you should be fine. I have used the sapwood on mulberry bows, and if the tree is living, with undamaged sap, you should be fine.