I read that Celastrus scandens, not Solanum dulcamara, is the noninvasive variety.
Solanum dulcamara and Celastrus scandens are both known by the name "bittersweet" but they are entirely different plants. I discussed this previously; please see:
www.richters.com/questions-and-answers/06-20070324-1 Solanum dulcamara is listed in the WeedUS database (https://www.nps.gov/plants/alien/list/WeedUS.xls) as "invasive" in 7 states. The american bittersweet, Celastrus scandens, is not listed while a related asian species, C. orbiculatus, is listed (invasive in 22 states).
It is important to note that the WeedUS database includes many common garden plants that normally do not present a significant invasive risk when cultivated in gardens. Just about every common garden plant is a "weed" somewhere in the world.