Honeybees today may not be native to the New World, but I would like to point out that this didn't mean New World peoples didn't have honey.

This passage is taken from Sophie D. Coe's book America's First Cuisines pages 125-126.

One thing the expedition of Francisco Hernandez de Cordoba noticed on the island of Cozumel, and later in Yucatan, may still be seen in those places today by the visitor. It was, and is, an excellent place for honey production. Today the honey is produced by the European honey bee (Apris mellifera), but prior to its introduction there were plenty of indigenous bees (Melipona sp., Trigona sp.) to do the job. Bee yards with thousands of hives are described by early travelers. Hernandez de Cordoba was said to have seen many wooden hives and to have been brought calabashes full of white and excellent honey. Honey was one of the principal products of the country and along with locally produced cotton cloth was traded far and wide in Mesoamerica. Among the Maya it was used to sweeten some of the maize drinks, the posolli and atolli, and to make an exceedingly important alcoholic ritual beverage, balche. The fact that a good part of one of the four surviving Maya books, the Madrid Codex, is concerned with bees and bee keeping underscores their importance.