@ forsoothe - check wikipedia or Flora of North America. Morus alba IS NOT native to north america. It is called Russian mulberry for a reason.
The North American native mulberry is the Red mulberry.
The widely invasive white mulberry aka Russian mulberry, Morus alba, is found "everywhere", and it does hybridize with native Morus rubra and the other invasive mulberry, Morus nigra. Morus nigra is only winter hardy through zone 7, so it is an invasive in southern North America.
floranorthamerica.org
floranorthamerica.org
floranorthamerica.org
@Darth Masiah - nice starts. I do think you have white mulberry, aka Russian mulberry. Or you have a hybrid that favors white mulberry in appearance. As mentioned by others, they do work well for bonsai, regardless of what species they are.