You are living within a mile of probably a hundred mulberry trees right now. I say this as someone who goes through Broome County NY fairly often.
If you know what a mulberry tree looks like you will notice them everywhere. They are common along roads, trails, farms, suburbs, anywhere. In June they will be dropping gazillions of fruits everywhere. The road will be stained purple under them, etc... So spend the next few weeks, while the leaves are still on, and identify several trees. (It is easiest with the leaves on). Make certain that you know exactly which trees they are so you can still find them when they lose their leaves and go dormant. Then take cuttings of them once they go dormant (that is the best time for cuttings). Carefully label each cutting with the location of the source tree from which you cut it. Then get them rooting over the winter (mulberries are among the easiest to
root).
Then next June when the trees start dropping fruit, visit each of your source trees from which you took cuttings, and make a note of which trees are fruiting. These are your females. Go home, check the labels on your rooted cuttings, and save the one(s) that came from a female. This way you are taking the cuttings now (well, soon anyway), rooting them all winter, and by the time you are seeing actual fruits on the trees you ought to have several well-rooted cuttings ready to transplant. As long as you are good at labelling your cuttings and remembering which tree you cut them from, it will just be a matter of visiting the "mother/father" trees next June to see which ones are female. Toss out the cuttings that came from males, and plant the best looking, strongest female(s).
If it just happens that all of your cuttings came from males, just keep driving around until you find a fruiting female (do it in June and you will find one). This will mean it takes you an extra year to get the right cutting, but mulberries grow pretty fast.
I hope I am making sense.
This method is free
This method does not rely on shipping a young seedling in a
cardboard box around the continent
This method virtually guarantees you get a female (if you take cuttings from several trees and successfully root them. Just keep your labels accurate and are careful to visit the source trees during fruiting season)
This method lets you choose a variety of mulberry that is already growing productively in your neighborhood
This method will not work if you are hoping for a specific kind of "brand name" mulberry, but it will be fine if you just want a general "wild" one.
Obviously get permission from the landowner before taking cuttings if they are in someone's
yard.
Good luck
Edited for spelling