Does the Catholic Church agree with the criteria for bishops in I Timothy 3:2-5?
Yes: "2 It behoveth therefore a bishop to be blameless, the husband of one wife, sober, prudent, of good behaviour, chaste, given to hospitality, a teacher, 3 Not given to wine, no striker, but modest, not quarrelsome, not covetous, but 4 One that ruleth well his own house, having his children in subjection with all chastity. 5 But if a man know not how to rule his own house, how shall he take care of the church of God?
2 "Of one wife"... The meaning is not that every bishop should have a wife (for St. Paul himself had none), but that no one should be admitted to the holy orders of bishop, priest, or deacon, who had been married more than once. "