The Online Etymology Dictionary says "bull's-eye" was first used to describe "center for target" in 1833. While Wordsmith.org speculates that's due to the "earlier agro-economy and the importance of bovine animals," I am inclined to believe the origin described by The Word Detective. They claim the popular use of the term for pretty much anything small and round began in the 17th century. Often, it included a protruding lump in the center, but not always. Why a bull instead of a cow, chicken, or goat? Unfortunately, nobody knows.
Certainly nobody questions the term's versatility. It can describe the center circle of a target, a lens of short focal distance, a circular window, a piece of glass inserted in a ship's deck, and a round piece of hard candy. Considering my luck with the dartboard, maybe I'll just take the candy.