A. THE RISE OF THE BISHOP
The word bishop appears four times in the New Testament in the King James Version (1Tim. 3:1, 2; Titus 1:7; 1Peter 2:25). Modern translations render the Greek word episkopos as overseer (NIV), or elder (NCV). The term bishop that has been used by some branches of the Church since the second century. Thus this word identified an ecclesiastical office by the time the King James translators had commenced their work. It is suggested that the translators were obliged to incorporate this word into their translation to justify such an office being in the State Church. Cursory examination of the texts where the King James version uses the term bishop readily shows that this word indicates a leadership function more akin to what most would identify as an elder.
Therefore, knowing this, we must put aside this insight, and examine how the second century Church appears to have used the term.
(i) THE ORIGIN OF THE BISHOP
According to the Church of Rome (formerly stated in the Council of Trent), Bishops existed from the beginning in the New Testament Church.  Chrysostom (c. 350 - 407) identified them with the episkopos or presbyteros (an alternative New Testament word). He wrote, “presbyters of old were called bishops...and the bishops presbyters.”  What is surprising is how quickly bishops became a religious order, or cleros (from where we get the word clergy).
The apostles took the initiative in the development of other offices in the church when they were so directed by the Holy Spirit. This does not by any means imply a pyramidal hierarchy, such as the Roman Catholic church has developed, because the new officials were to be chosen by the people, ordained by the apostles, and have special spiritual qualifications that involved leadership by the Holy Spirit...There was to be no special class of priests set apart to minister a sacerdotal system of salvation because both the officials and the members of the church were spiritual priests with the right of direct access to God through Christ (Eph. 2:8-9). 
Professor Cairn’s above statement describes the Church nearing the end of the first century. As we investigate the origin of the bishop, we acknowledge that the position of elder was referred to as a bishop by the second century. But by the third century, the term bishop came to mean something else.
The transformation of the bishop from being an elder to being a pseudo-apostle originated in response to the heresies propagated by Marcion and others, notably Valentinus. Marcion taught that the Old Testament was not divinely inspired, and consequently all references to the Old Testament within the New Testament must have been corruptions instigated by Judaisers, whom Paul warned against in his epistle to the Galatians.  Valentinus, on the other hand, taught that only some the Old Testament was inspired, and some was included because of the hardness of men’s hearts. He taught that Jesus secretly taught His disciples certain things that were only ever committed to oral tradition. 
How could these errors be refuted by the early Church? The apostles had been the guardians of the truth and sound doctrine. But with their passing and the emergence of the second century, how could the Church truly know what was sound apostolic teaching? Ignatius (who lived toward the end of the first century and was martyred early in the second century  ) was the third bishop of Antioch. He was the first to suggest that the local bishop be regarded as the rightful source of sound doctrine.
These comments came after Clement (30 - 100), one of the bishops of Rome, had written to the church at Corinth, in 96 AD,  and urged them to submit to their bishop.  Thus, it seems that the position of bishop initially changed in prominence for all good intentions. If bishops could be seen and promoted as the authorised teachers of apostolic doctrine, then the Church stood a better chance of repelling heresies, and perhaps more importantly maintaining unity.
(ii) APOSTOLIC SUCCESSION
But in striving to maintain sound doctrine and unity, the role of the bishop changed from its original concept of an elder/overseer. In the absence of the first century apostles, who formed the critical function in the leadership structure of the Primitive Church, the second century Church was now void of this vital functional leadership. The Church has always been reluctant to foist the title apostle on anyone other than those mentioned in the New Testament. But it will be seen that the leadership structure of the early New Testament Church was more than a foundational structure: it was a divinely ordered, prescriptive leadership structure. Consequently, when the first century apostles died, there arose a need to fill the void. And it was the bishops of the churches that organised themselves to fill the void.
By the turn of the second century, Bishops justified their rightful place to succeed the apostles by arguing that although all bishops (episkopos) were elders (presbuteros), not all elders were bishops.  The Church of Rome has always stated that Peter was the first Bishop of Rome.  This position then unconsciously identified succeeding bishops as the rightful successors to the original apostles. While all bishops were originally considered equal, and thus succeeding the original apostles, the bishop of Rome came to a unique prominence due to the church’s size, strategic location, and belief that the succeeding bishops replaced Peter who was the founding ‘rock’ of the Church. 
The main point to be made about the belief in apostolic succession, is that in the second century the term bishop came to be a synonym for the governmental aspect of the first century apostle. While the first century apostles are assigned a unique place of honour in the history of the Church, the reality is that their governing ministry was continued by the newly defined bishops of the second century. Because these bishops rose above their brother elders within each church, they are identified as monarchical bishops. Eventually these monarchical bishops rose even higher in authority than their former co-elders by becoming responsible for several local churches. They consequentially fulfilled the original governmental apostolic function even more closely.
Professor Chadwick feels that there were four factors in the rise of the monarchical bishop: 
Initially, there was a clear understanding that bishops were the custodians of apostolic doctrine, and the churches they had founded. But by the middle of the third century, the bishop of Carthage, Cyprian (248-58) openly advocated that bishops were the personal successors of the apostles.  Theologically, we are faced with two glaring problems to this teaching. Firstly, the New Testament makes no mention of succession (diadoché) of the apostolic authority by the laying on of hands and prayer (as the Roman Church teaches). Secondly, the idea is absent for most of the second century, which presumably would be the critical period for this teaching’s development. But the fact remains that the redefined bishops of the second century did fill the void created by the death of the first apostles. Eventually the Roman Church narrowed their doctrine of apostolic succession to the bishop of Rome. 
The danger in refuting the erroneous doctrine of apostolic succession is that we may view the ministry of the apostle as limited to the Twelve Apostles of the Lamb, and ignore that the ministry of the apostle has actually continued within the church regardless. Thus Hans Küng could be considered to inadvertently eisegete the ministry of the apostle while refuting apostolic succession -
The rise of the bishop’s prominence through the second century, to assume the governmental aspects of the original apostles, is a strong argument for suggesting that the apostle was intended as a universal, rather than as a dispensational ministry. That is, the rise of the bishop tends to indicate that the function of the original apostles was a divinely ordained ministry of Church leadership for all time.