Are you talking about the decorative vine with the orange berries? If so, I've never seen a tomato/tobacco worm on it.
Weird, the Bittersweet in Wikipedia doesn't look like the same bittersweet we have growing locally. And after searching around there are two forms of Bittersweet, the Oriental (non-native, nightshade relative) and the American (native, non-nightshade relative).
Hornworms can be cultivated on just about anything. I know when I purchased some as a variety food source for my Bearded Dragon they recommended mulberry tree leaves, which commonly grow around here and the worms did just dandy.
But I don't think they would be found on other nightshade-type plants due to the plant size differences. One large tomato worm can decimate a large tomato or tobacco plant in a few days, most other nightshades don't grow in thickets, at least around here, and to eat with such gusto would clearly spell demise for the worm.
Yeah I dont know which one it is, it might be the non nightshade one then. The plant invaded large bushes, and grow in every corner and on every fence before they are cut down, so there would be enough for a few hornworms, but the vine is flimsy so a hornworm's body weight probably wouldnt be supported on it.
They really eat mulberry leaves? We have tons of white mulberrys here.