The late Greg Bahnsen provided a good outline demonstrating the biblical basis for the Presbyterian governance we follow:
Christ directs his church through the Scriptures, His own self-revelation and authoritative guidance. Let me offer here a brief summary of the biblical material which I believe is relevant to determining how Christ would have His church governed. The Bible is not silent on this matter.
1. There is no distinction between “elders” and “bishops” (Titus 1:5-7; Acts 20:17,28); these represent the same office and order.
2. Each congregation and center of leadership is to have a plurality of elders (Acts 14:23; 20:17; Phil. 1:1), not one-man rule.
3. These elders have oversight of the church (Acts 20:28; I Pet. 5:2-3) and are thus responsible to rule the congregation (I Tim. 3:5; 5:17; I Thes. 5:12; Heb. 13:7, 17, 24).
4. They judge among the brothers (cf. I Cor. 6:5) and, in contrast to all the members, they do the rebuking (I Tim. 5:20). Christ calls them to use the “keys of the kingdom” to bind and loose (Matt.16: 19; 18: 18; John 20: 23)—these keys being the preaching of the gospel (I John I :3), administering of the sacraments (Matt. 28:19-20; I Cor. 11: 23ff.), and the exercise of discipline (Matt. 18:17; I Cor. 5:1-5).
5. The elders are assisted in their ministry by “deacons” who give attention to the ministry of mercy (Phil. 1:1; Acts 6:1-6; cf. I Tim. 3:8-13).
6. The office-bearers in the church are nominated and elected by the members of the congregation (e.g. Acts 6:5-6), but must also be examined, confirmed and ordained by the present board of elders (Acts 6:6; 13: 1-3; I Tim. 4: 14).
7. Members of the church have the right to appeal disputed matters in the congregation to their elders for resolution, and if the dispute is with those local elders, to appeal to the regional governing body (the presbytery) or, beyond that, to the whole general assembly (Acts 15). The decisions of the wider governing bodies are authoritative in all the local congregations (Acts 15:22-23, 28, 30; 16:1-5).