I don’t think that the passage in Timothy indicates there is only one bishop in a city because Paul is writing about the qualifications of for an
individual to become an overseer. It would make no sense to say, “If a man aspires to the office of overseers.”
It might be good to find out first of all if there is a distinction between elders and bishops. One evidence that they are equivalent is in Titus 1:5,7, where first elders are to be appointed in every city and then Paul writes, “For the bishop must be blameless, etc.”
This is somewhat confusing because, while elder and overseer are seen to be equated, he says to appoint “elders” and not “an elder” in every city, but there is a definite article before bishop.
Another place where elders and bishops are equated is in Acts 20:17, 28. Paul called the elders of the church in Ephesus to come to him and in vs. 28 says that God had made them overseers.
A third place where elders are seen to exercise the oversight is in 1 Peter 5:1,2, where he addresses “the elders who are among you” (calling himself an elder) and then speaks of them exercising oversight, with the word
episkopeo, which is the verb form that corresponds to the office of overseer/bishop,
episcope.
I can’t find any place to make a distinction between elders and bishops, and while there are elders and deacons spoken of together I can’t find elders and bishops together.
Paul called the “elders” from the church in Ephesus, neither the “elder of the church” nor the “elders of the churches.” When he wrote to the Philippians he addressed “the bishops and deacons”, plural. When James took up the topic of illness, he said to call in the “elders of the church and let them pray . . .” (5:14).
Elders are always plural in the Bible, whether it’s the village elders, the Sanhedrin, or the church elders in Jerusalem, or the 24 elders before the Throne. That is, they are spoken of as forming a group. Elders form collective councils. Unless I’m mistaken, there is never a head elder spoken of as being over a council of elders.
From James it is clear that there are multiple elders in a place and, again, they are collective. He doesn’t say to bring in an elder to pray. If elders are bishops and vice versa, then here he cannot be talking about elders from different dioceses. The poor sick person could well die before they could reach him. They have to be local and plural.
If we want to say Peter was a bishop, I don’t see we can do so from scripture any other way than taking the cited passage above where he calls himself an elder and then say he was a bishop because he speaks of elders exercising “bishoply”

oversight.
But then Paul spoke of “the bishop” to Titus. Then again, John identified himself as “the elder” in his 2nd and 3rd letters. I feel a need for someone who really knows Greek here because I am not sure if the definite article works the same as in English. Some translations, including the King James, have “a bishop’ instead of “the bishop”.
With John there would be a problem if we think he was saying he’s somehow the only elder there is or the top elder, and which would run against the preponderance of scripture in regard to elders. (It would also seem to upstage Peter, if we assume John is taking pre-eminence.) There has to be another interpretation of his referring to himself this way.
The same principle would apply to Paul in Titus. A single verse cannot override the preponderance of scripture. Elders are plural and form collective groups. Elders in the New Testament (which is our only record of the apostolic period) are bishops, exercising local oversight.
There is no place in the New Testament where a single man is in charge of a local assembly, except one, and it is bad, not good. This is Diotrephes in 3 John.
I hope this is clear and will be read with an open understanding.
Yours in Christ,
Melville