Evidence that Peter alone was made a Bishop by Christ? This got my attention. Although I don't currently agree with it, it's an intriguing question which I am open to accept if sufficient evidence is found. Now when I read classical works on the Papacy (or general catholic works on Ecclesiology), I'm starting to see sort of how St. Robert Bellarmine came to that conclusion. Some of the "evidence" I've found so far are Saurez's Defensio Fidei Catholicae (taken as a whole) and Sermons by St's. Gregory the Great and Leo the Great. 

For example,


  "When the Passion of the Lord was drawing near, an event
  that was going to shake the constancy of his disciples, he said:
  'Simon, Simon. Behold, Satan has obtained his request to sift
  you (all) like wheat. I, however, have begged for you that your
  faith not fail. Once you have converted, strengthen your brethren,
  lest you (all) enter into temptation.' Each apostle encountered
  the same danger through temptation from fear. All
  equally needed the help of divine protection, since the devil
  wanted to harass them all and to crush them all. Still, the Lord
  took special care of Peter and prayed especially for Peter. It
  was as if the condition of the others would be more secure if
  the mind of their leader were not overcome.
  In Peter, therefore, the fortitude of all is reinforced, for the
  aid of divine grace is ordered in such a way that the firmness
  given to Peter through Christ is conferred upon the apostles
  through Peter."" (Tractatus IV, Pars 3, Sancti Leonis Magni).


Now, I'm not arguing that that quote alone proves the thesis but combined with other arguments in context may give some weight. Does anyone have any evidence for St. Robert Bellarmine's claim? Any arguments against it?
St. Robert's opinion that St. Peter consecrated the other Apostles bishops doesn't seem common. For example, D. I. Lanslots, O.S.B., says in his The Primitive Church: The Church in the Days of the Apostles ch. 15:


  Christ directly consecrated His Apostles bishops; they and their successors were to consecrate all others.


The "Apostolic College" Catholic Encyclopedia entry distinguishes "Apostle" and "bishop":


  Although both, bishops and Apostles, are appointed by Divine authority, yet the Apostles received their commission immediately from Christ, whereas the bishops receive theirs but mediately, i.e. through the medium of human authority. The power of order and jurisdiction is the same in the Apostles and in their successors, but, whereas the Apostles receive it from the Divine Founder Himself, the bishops receive it through the channel of other bishops. Immediate commission implies, in the missionary, the power to produce, at first hand, credentials to prove that he is the envoy of God by doing works which God alone can work. Hence the charisma, or gift, of miracles granted to the Apostles, but withheld from the generality of their successors whose mission is sufficiently accredited through their connection with the original Apostolate.