Ask Mr. Smarty Plants

Yes, there are conflicting answers about the toxicity of the nectar from Carolina jessamine to honey bees. There is very little actual scientific research on the internet (see the one published article below) about this issue and lots of general statements. So I can see your confusion. My advice would be that if there are few flowers blooming in your neighborhood when the Carolina Jessamine are blooming that more honey bees will be attracted to it and if there are detrimental effects to their foraging then they will be more severe. If there are many more nectar plants in bloom at the same time then the bees have plenty of safe plants to visit and your vine should have little effect on them. But there some serious toxicity issues with this plant for humans and animals so that may weigh in heavy on your decision too.
Here’s some information from our website about this native vine. Native from Virginia and Florida west to Arkansas and east Texas and south to Guatemala, Carolina jessamine is a twining, evergreen vine, 10-20 ft. long, that will climb trees, scramble over fences and structures, or develop a mound of tangled stems if left to its own devices. Lustrous, dark-green foliage develops a slight yellow or purple cast in winter. Axillary clusters of very fragrant, yellow, trumpet-shaped flowers. The fruit is a 1 1/2 in. long capsule.
This high-climbing vine is very common in parts of the South, frequently found in abandoned fields and climbing high into the canopies of pine forests. It is quite adaptable and tenacious, with no serious disease or insect problems. These qualities, along with its glossy, evergreen leaves and waxy, trumpet-shaped flowers, have made it a mainstay of the suburban landscape in the Southeast. The flowers, leaves, and roots are poisonous and may be lethal to livestock.
Usually blooms briefly in early spring, but can start as early as December and then bloom again briefly in early fall.
The North Carolina Museum of Sciences website discusses Carolina jessamine and the bee and human toxicity aspect of the plant.  They say, in spite of its popularity with gardeners, all parts of the Carolina jessamine contains strychnine-like toxins that can make people sick if the plant is accidentally or intentionally consumed or cause skin reactions in sensitive individuals. The flowers are similar in size and shape to honeysuckle, so children can be poisoned if they suck nectar from jessamine flowers. However, their toxicity also means that many species of grazers will avoid eating jessamine, including deer, which may partially account for their popularity in home gardens.
The toxins in the nectar do not deter pollinators, however. The nectar is reportedly toxic to honeybees, but we commonly see Eastern tiger swallowtails and Eastern carpenter bees slurping nectar from the Prairie Ridge flowers, as well as a variety of other butterflies and bees. Large bees, such as the carpenter bees and several bumblebee species, are too large to fit inside the flower, so they “rob” them by chewing holes near the base of the trumpets and sucking the nectar out without pollinating the flowers. Nectar robbing is a common behavior in bumblebees and other large bees when they visit trumpet flowers, so look for them sitting at the base of Jessamine flowers if you want to see this fascinating behavior!
And from the American Honey Plants, Frank C. Pellett, 1920 American Bee Journal ...
The yellow jasmine is a well-known poisonous climbing vine common to the Southern States from Virginia to Florida and west to Mexico. Its yellow flowers, in short axillary clusters, appear in early spring (February and March) and are very fragrant. The vine climbs over trees to a great height, often 30 feet or more. It yields pollen and probably some nectar. It is reported as poisonous to the bees.
"For the past nine years I have observed, commencing with the opening of the yellow jasmine flowers, a very fatal disease attacking the young bees and continuing until the cessation of the bloom. The malady would then cease as quickly as it came. The symptoms of the poisoning are: The abdomen becomes very much distended, and the bees act as though intoxicated. There is great loss of muscular power. The bee, unless too far gone, slowly crawls out of the hive and very soon expires. The deaths in twenty-four hours, in strong stocks with much hatching brood, may amount to one-half pint, often much more. My observations have been verified by dozens of intelligent beekeepers breeding pure Italians where Gelsemium abounds."—Dr. J. P. H. Brown, American Bee Journal, Nov., 1879.
And finally, several scientists from Dartmouth College tested the nectar, gelsemine that is found in the Carolina Jessamine and published an article in Ecological Entomology (2008), DOI: 10.1111/j.1365-2311.2007.00974.x In this study, natural and experimental concentrations of a nectar alkaloid, gelsemine, had no effect on the performance of Osmia offspring under the experimental conditions studied. Although the alkaloid is toxic to vertebrates (Kingsbury, 1964), potentially toxic to non-native honey bees (Burnside & Vansell, 1936), and deterrent to native Osmia adults (Adler & Irwin, 2005), offspring of Osmia were not affected by even unnaturally high concentrations of the alkaloid.