The symbolism actually comes almost entirely from Brigham Young's fascination with one simple verse in the Book of Mormon.
And they did also carry with them deseret, which, by interpretation, is a honey bee; and thus they did carry with them swarms of bees, and all manner of that which was upon the face of the land, seeds of every kind.
When Brigham Young worked to establish Mormon colonies throughout the Inter-Mountain West region, the colony eventually petitioned the US government for statehood. Brigham Young decided that the territory should be called "Deseret," because he saw the honeybee's industriousness and self-sufficiency as admirable and worthy of emulation. The proposed State of Deseret was enormous, covering almost all of modern-day Utah and Nevada, and smaller portions of the surrounding states, and Congress ended up denying the petition, and instead allowing statehood to smaller regions. However, to this day, a beehive icon titled INDUSTRY figures prominently in the official seal of the state of Utah, also known as "the beehive state."
The term Deseret is used in many parts of Mormon culture, particularly in Utah. (See the Wikipedia disambiguation page for several prominent examples.)
It's worth noting that 20th century scholarship and research into ancient Egyptian language and culture has discovered that honeybees were held in extremely high regard by the Pharaohs, and the word DSR.T (vowels removed, as they were not part of the written language) was associated with them. (Nibley, "The Deseret Connection", Abraham In Egypt)
Within the church, the beehive symbol is easily recognizable, but is not particularly common. For example, the pulpit at the Conference Center is decorated with a beehive icon, as noted in the question, but in most local chapels it is not present on the pulpit.