David Livingston wrote:Far be it for me to argue with Joseph
but I will I have never come across Mulberrys having different sex trees like hollys everyone I have seen seems to be hermaphrodite. ( good word for scrabble that )
Since comercial types hybridise with your native red mulberrys its anyones guess what you have
I would take some hardwood cuttings and graft on some black mulberry 
My birdie planted tree has both male and female flowers every spring. Opposing flowers occur on the same branches. We harvested 3 gallons of berries this year.
It took only 4 years to begin fruiting. I have another tree about 10 years old that has not fruited. I will be grafting this one. I haven't decided whether to get ever bearing Illinois, or propagate mine. David, why do you suggest black mulberry?