Correct me if I am wrong but the bible has a role "Overseer", but no role of Priest in the NT. And as I see it the role of Bishop has evolved out of the unbiblical role of Priest. If we are to be biblically correct, there are zero 'intermediaries' between the Believer and God.
A priest is someone who administrates God’s current covenant. To that end, we are all, male and female, priests of God - royal priests, in fact. This is not just that we serve at the pleasure of the King, but that we are of His familial line, too.
As far as intermediaries go… there is One who is in all who believe, the Holy Spirit. This gives all in Christ the right to handle any measure of grace they are given. Now, by handling this grace wisdom is gained. Because we function as One Body, it is expected that those who operate within more grace make that grace available to others. Built into the Body is the need for each part, functioning as God intended, to work in support of the other parts.
As we mature in spiritual matters more will be given. It is expected that the mature will work to support the immature. It is also expected that the immature look to the mature for guidance. The mature, then, must give an account for those whose souls are watched over. Jesus gave an account for 12 souls. How many do you think a person, today, might be able to watched over effectively?