The Collaborative International Dictionary of English v.0.48:

Bye \Bye\ (b[imac]), n.
   1. A thing not directly aimed at; something which is a
      secondary object of regard; an object by the way, etc.; as
      in on or upon the bye, i. e., in passing; indirectly; by
      implication. [Obs. except in the phrase by the bye.]
      [1913 Webster]

            The Synod of Dort condemneth upon the bye even the
            discipline of the Church of England.  --Fuller.
      [1913 Webster]

   2. (Cricket) A run made upon a missed ball; as, to steal a
      bye. --T. Hughes.
      [1913 Webster]

   3. In various sports in which the contestants are drawn in
      pairs, the position or turn of one left with no opponent
      in consequence of an odd number being engaged; as, to draw
      a bye in a round of a tennis tournament.
      [Webster 1913 Suppl.]

   4. (Golf) The hole or holes of a stipulated course remaining
      unplayed at the end of a match.
      [1913 Webster]

   By the bye, in passing; by way of digression; apropos to
      the matter in hand. [Written also by the by.]
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Bye \Bye\ (b[imac]) n. [AS. b[=y]; cf. Icel. byg[eth] dwelling,
   byggja, b[=u]a, to dwell [root]97.]
   1. A dwelling. --Gibson.
      [1913 Webster]

   2. In certain games, a station or place of an individual
      player. --Emerson.
      [1913 Webster]

WordNet (r) 3.0 (2006):

bye
    n 1: you advance to the next round in a tournament without
         playing an opponent; "he had a bye in the first round"
         [syn: bye, pass]
    2: a farewell remark; "they said their good-byes" [syn: adieu,
       adios, arrivederci, auf wiedersehen, au revoir,
       bye, bye-bye, cheerio, good-by, goodby, good-bye,
       goodbye, good day, sayonara, so long]