No, a bishop does not need to be married or have children. The Lord Jesus is described as a ‘bishop’ (an ‘overseer’) in 1Peter 2:25:
For you were straying like sheep, but have now returned to the Shepherd and Overseer [bishop] of your souls.
However, the Lord Jesus never married or had children; so, a bishop does not need to be married or have children.
The requirements in 1Tim. 3 (and Titus 1:6) are written in such a way as to insist that a bishop who is married must be the husband of only one wife,1 and that a bishop who does have children must be a father who his children respect and obey. If someone is not married or does not have children (like the Lord Jesus wasn’t married and didn’t have children), then these elements do not apply to them if they desire to be a bishop.
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Footnotes
1. See What does “wife of one husband” mean in 1Tim.5:9?
Jesus is not a temporary overseer of a congregation of believers – he is the son of God and permanent master of all believers. He was a “special appointment”, as was Paul himself. However, Paul, when writing to Timothy and Titus uses a very clear and simple argument that if men are to be leaders of congregations, they should be qualified as good leaders of families. He uses the logic that demands this qualification be applied to all potential leaders: if he cannot manage his household with dignity and keep his children submissive, how can he care for God’s people? (1 Timothy 3:4-5). In Titus 1:6, the requirement that he be the husband of one wife is repeated along with the requirement that his children should be believers and not open to charges of misbehaviour. Paul includes some requirements that are very visible and easy to judge (such as this requirement) and others which are more subtle and more difficult to measure (such as being above reproach – also from Titus 1:6). In selecting such elders or overseers, Titus and Timothy would have both the obvious and the less obvious clues to go on. No believers would completely satisfy all of the requirements and selection would be based on some sort of overall assessment – “by their fruits you will know them”.
In these related passages, Paul could very easily have said “If a man is married, he must have only one wife”. Instead, he chooses on both occasions to say “the husband of one wife” as the second in his list of requirements. A conditional requirement that only applied to some people would not have that position of importance in the list – nor is this expressed as a conditional requirement. It could be reasonable to ask how this requirement would be applied to widowers whose “one wife” has died, but not to dismiss it completely as not relevant to men who have never been married.
I realise that this comment is already far too long :), but have you ever asked why having 2 or more wives was not allowed for elders/overseers? It bears thinking about in relation to this question/answer.
My question is: Is a Bishop-Elect suppose to be married.