According to word-detective.com: Since the 17th century, “bull’s-eye” has been used as a term for almost anything small and circular, especially if it protrudes slightly, forming a hemispherical bump resembling the protruding eye of a bull or cow. Thus, at various times, “bull’s-eye” has been used to designate a thick piece of glass set into the deck of a ship to illuminate the lower decks, a one-crown coin of British currency, a globular piece of candy, and a small circular window, among other things. So although the spot in the center of a target doesn’t protrude like a real “bull’s eye,” it is small and circular and thus fit the popular definition of “bull’s-eye.”
There is also speculation that the “bull” part may derive from Latin “bulla” which means root or small round object.