I believe Paul was describing an office more similar to elders
(presbyter) than the bishop today.
Let's examine the verses in their context.
Titus 1
5 I left you behind in Crete for this reason, that you should put
in order what remained to be done, and should appoint elders in
every town, as I directed you: 6someone who is blameless, married
only once,* whose children are believers, not accused of debauchery
and not rebellious. 7For a bishop,* as Gods steward, must be
blameless; he must not be arrogant or quick-tempered or addicted to
wine or violent or greedy for gain; 8but he must be hospitable, a
lover of goodness, prudent, upright, devout, and self-controlled.
9He must have a firm grasp of the word that is trustworthy in
accordance with the teaching, so that he may be able both to preach
with sound doctrine and to refute those who contradict it.
I believe Paul was describing the same office here, though
'elders' and 'bishop' are used.
Notice Paul stressed that elders are married. (impt later .. read
below)
1Tim 3
The saying is sure:* whoever aspires to the office of bishop*
desires a noble task. 2Now a bishop* must be above reproach,
married only once,* temperate, sensible, respectable, hospitable,
an apt teacher, 3not a drunkard, not violent but gentle, not
quarrelsome, and not a lover of money. 4He must manage his own
household well, keeping his children submissive and respectful in
every way 5for if someone does not know how to manage his own
household, how can he take care of Gods church? 6He must not be a
recent convert, or he may be puffed up with conceit and fall into
the condemnation of the devil. 7Moreover, he must be well thought
of by outsiders, so that he may not fall into disgrace and the
snare of the devil.
While only 'bishop' is described here, notice how similar it is
to the description in Titus. And bishops should be married only
once.
From verse 8, Paul talks about deacons. (refer to Calvin's fourfold
office)
Phil 1
Paul and Timothy, servants* of Christ Jesus,
To all the saints in Christ Jesus who are in Philippi, with the
bishops* and deacons
Yup, once again bishops and deacons.
To reiterate, my point is that the office of bishop is not
mentioned in Scripture.