I'm not familiar with Nebraska, but the only native mulberry we have here in the East is Red Mulberry (Morus rubra). Asian White Mulberry is also naturalized here and there across the country, as well as paper mulberry. I've only used red mulberry, and it's great wood. Like Justin said, osage is in the mulberry family. Mulberry is not as dense as osage, just make the bow a bit wider/thicker for the same draw weight than you would with osage.