Just as the Jaredites collected birds and fish, they also collected seeds and insects. Honeybees were particularly useful and were indigenous to the Americas prior to the arrival of Europeans. The Maya of the Yucatán kept stingless bees (Melliponabeecheii). But there is no indication that native American bees are related to Old World species.
While we cannot say that the Jaredite bees contributed to apiculture in the New World, it is possible to speculate that the Jaredite record mentions bees because it was one of the few fauna they would have known in both places. Possibly Ether’s mention of bees derives not only from their usefulness but from their symbolic ties to the Old World.