The evidence from the Bible shows that initially the terms for 'bishop' and 'presbyter' were used interchangeably to describe the same office in the Church. However, it must be kept in mind that the Scriptures were written during the time when the Apostles were still alive and were the de facto overseers (or acting bishops) over the whole church. In fact, one can see the transition beginning even in ACTS to what would become the pattern for monoepiscopacy that would ultimately followed by all the local churches.
This transition is seen midway in Luke's account at the Church of Jerusalam after the apostles are dispersed by the persecution. From that point on we see references to 'James and the elders with him'. The Lord's brother was basically the chief pastor (or bishop/presbyter) of the Jerusalem church, which can be clearly seen by his role in the council of Jerusalem among other things. So even though the terms continued to be interchangeable for a while (particularly in the Western Churches), the basic pattern of one 'chief bishop/presbyter with his associate bishop/presbyters' was set while the apostles were still alive. We know from Eusebius, that James was succeeded in his 'episcopal office' by his cousin Simeon, and from then on there continued to be one particular man who was seen as THE 'bishop' at a time. By the early 2nd century, Ignatius was using the terms 'bishop' and 'presbyter' to refer to the distinct offices--the 'chief shepherd' and the 'associate/assistant shepherds', if you will--and he named a few of them in the letters he wrote on his way to his martyrdom (including Polycarp). Even in Rome, where the terms remained interchangeable for good while longer, there was according to Eusebius an historical record of one man holding the 'episcopal office' (even if he used the term anachronistically) at time going back to the Apostles and starting with Linus.
BTW--the roles of Timothy and Titus are also important in understanding the development of the monoepiscopacy. Here were two men, who weren't Apostles themselves, but who had authority from the apostles to appoint/ordain elders/overseers in their respective locations (Ephesus and Crete). They were regarded by Eusebius (and presumably by the sources he used) as the first 'Bishops' of Ephesus and Crete. No doubt, other apostolic co-workers had similar oversight roles in other cities on behalf of the Apostles.