Reading Leviticus 4:15-18, you will see a close parallel with earlier: 4:4-7 (also in Forgiveness is not ‘cheap’, what is its cost?). In this later section on the unintended sins of the congregation (verse 15-18), the elder began the sacrificial ritual, which was then continued by the Priest.
The killing of the bull by the elders was about the congregation (of which the elders are representatives) taking active, and central, part in seeking forgiveness. In any case, the elders, or the leaders of our congregation, have this role to seek forgiveness from God for the congregation. It cannot be a member who is not an elder, nor someone who is not part of the congregation. It ought to be wholly representing the congregation to seek forgiveness such that forgiveness to the congregation is whole. There could well be many variations of implementation on this in the modern church, perhaps being sensitive to culture and customs as well as structure of church.