Q.how to transplant bittersweet vine
How to determine male from female and best time of year to transplant?

Here is an article with basic growing information: https://www.gardeningknowhow.com/ornamental/vines/bittersweet/growing-bittersweet-vines.htm
To add a little bit, the female flower has a rounded knob in the center of the flower, with no pollen; the male has several short stamens with yellow pollen on the ends. Some flowers of both sex can sometimes be seen on one plant, but the majority of flowers will be one sex or the other.
Replanting is a bit tricky because or the very large and deep roots developed on plants that have been growing a long time; however, the best time to transplant is during dormancy, probably in late winter before growth starts, but the ground has thawed enough to dig. This article might help you: https://www.gardeningknowhow.com/ornamental/vines/bittersweet/growing-bittersweet-vines.htm