There are three plants named, "bittersweet"....
Image showing what bittersweet looks like in autumn, with its fall foliage and fruits.
American bittersweet is harmless, but Oriental bittersweet
(shown here) should be regarded as a weed, since it can harm your trees. The third type of weed that goes by this name ("bittersweet nightshade") is one of our most poisonous plants.