Is the bishop some far-off person in the initiation picture? Traditionally (by this I mean the early centuries, not 1962) the bishop was directly responsible in many ways, most especially discernment with Christians-to-be and in the liturgies of the catechumenate. Here’s what the modern rite has to say:
12. The bishop, (see Christian Initiation, General Introduction, 12) in person or through his delegate, sets up, regulates, and promotes the program of pastoral formation for catechumens and admits the candidates to their election and to the sacraments. It is hoped that, presiding if possible at the Lenten liturgy, he will himself celebrate the rite of election and, at the Easter Vigil, the sacraments of initiation, at least for the initiation of those who are fourteen years old or older. Finally, when pastoral care requires, the bishop should depute catechists, truly worthy and properly prepared, to celebrate the minor exorcisms (nos. 90-94) and the blessings of the catechumens (nos. 95-97).
The rule of thumb seems to be that the bishop comes to the fore just as the godparents are confirmed and beginning their public ministry with the elect. It’s interesting that the rite so strongly designates the bishop to preside at the Easter Vigil. I wouldn’t have ever thought it was even a question.
Note the bishop’s responsibility to “depute” catechists to celebrate some of the minor rites: exorcisms and blessings, but not anointing (nos. 98-103). We’ll get to those minor rites later. This is one of the times at which lay people may give liturgical blessings in an authorized way. The bishop, not the pastor, is the one who oversees this ministry and is responsible.