This is just good old-fashioned orthography.  “Be gone!”  Imperative “be” followed by verbal adjective “gone”, used together so many times that the space between them retired.  We do not have “bego, bewent”, but neither do we have “isgone, wasgone”.  I am reminded of Beatrice in Much Ado About Nothing, Act IV, Scene 1 – “I am gone, though I am here.”

• 15.053 Begone now ere our arrows fly!

“begone, v.” OED Online. Oxford University Press, March 2015. Web. 7 May 2015.