What do you mean. I just talked to the parish about it. Why does the Bishop have anything to do with it in the first part?
In any given particular local church (diocese), the head is the bishop, and the parishes and their pastors’ authority derives from the bishop’s. Each bishop is required to have a process for the education of those to be granted the rites of Christian initiation: Baptism, Chrismation, First Confession, and First Eucharist. It will be a very different process in the various different rites, and slightly different amongst different sui iuris churches of the same rite. It may even vary between particular churches within the same sui iuris church.
The rite and sui iuris church in to which you choose to be accepted, Latin or Byzantine, determines which bishop is accepting you (possibly via his proxy, the Pastor). That bishop is the one who sets the nature of the process, and in very many ways, will be the successor to the apostles to whom you, as a catholic, are subject to the orders of.
Note that, in most of the US, the Latin church has opted for a regional synod developed and approved program called “RCIA” or “Rite of Christian Initiation for Adults”, a program which has provisions for both unbaptized converts (catechumens) and baptized converts (candidates). Some parishes combine the instructions, others do not; some diocese mandate one approach or the other.
In all cases, however, the Bishop is the arbiter of what is and is not acceptable liturgy in his/her diocese, subject only to the norms of the regional synod, their provincial metropolitan-archbishop, their patriarch, the Pope, and the Holy Synod of the Catholic Church. (Note that Latin rite provinces are either archbishop OR patriarch, while several eastern rite churches have patriarchs between the pope and their archbishops.)