Dallas says, "Spot on." I say, "Not quite." First off, bishops don't succeed apostles and never have. While a person may have been a bishop and then have been ordained an apostle, the two callings are distinct. Bishops were always called to preside over individual congregations, while the Apostles presided over the Church as a whole and were responsible for missionary efforts (assisted by groups of seventy men who traveled two by two, teaching the gospel).
I don't know if you've ever read anything about the medieval Church, but
"A World Lit Only By Fire" is a fascinating history written by William Manchester, Professor of History Emeritus at Wesleyan University. Believe me, apostolic succession in the early Church was nothing like Christ intended that it be!