According to the Federation Charter, which is as close to canon as we'll get probably... the Federation government IS bicameral. There is the Federation Council, which looks more like the UN Security council than a legislative body. But then there is the Supreme Assembly, which is composed of 1-5 representatives from each member world. See below.
Chapter IV: The Supreme Assembly
Composition
Article 9
The Supreme Assembly shall consist of all the members of the United Federation of Planets. Each member shall be entitled to have not more than five (5) representatives in this body;
Functions and Powers
Article 10
The Supreme Assembly may discuss any questions on any matters within the scope of the present Charter or relating to the powers and functions of any agencies provided for in the present Charter and, except as provided in Article 12, may make recommendations to the members and the Federation Council or both on any such questions or matters;
Article 11
The Supreme Assembly may consider the general principles of cooperation in maintaining interplanetary peace and security, including disarmament and the regulation of armaments, and may make recommendations with regard to such principles to the members or the Federation Council or to both;
The Supreme Assembly may discuss any questions relative to the maintenance of intergalactic peace and security put to it by any member or the Federation Council, or a nonmember planetary social system in accordance with Article 25 Paragraph 2 and, except as provided in Article 12, may make recommendations with regard to any such questions to the members, the Federation Council, or the pleading planetary social system, or to all of them. Any such question on which action is necessary shall be referred to the Federation Council by the supreme assembly either before or after discussion;
The Supreme Assembly may call situations which are likely to endanger the interplanetary and intergalactic peace and security to the attention of the Federation Council;
The powers of the Supreme Assembly as set forth in this Article shall not limit the scope of Article 10;
Article 12
Where the Federation Council is executing the functions assigned to it under the present Charter with respect to any dispute or situation, the Supreme Assembly shall make no recommendation with regard to that dispute or situation unless so requested by the Federation Council;
The President, with the consent of the Federation Council, shall notify the Supreme Assembly at each session of any matters relating to the maintenance of interplanetary peace and security which are under discussion in the Federation Council, and shall notify the Supreme Assembly, or the members if the Supreme Assembly is not in session, immediately when the Federation Council completes its deliberations on any such matters;
Article 13
The Supreme Assembly shall initiate studies and make recommendations for the purpose of:
Promoting interplanetary cooperation in political fields and encouraging the progressive development of interplanetary law and its codification;
Promoting interplanetary cooperation in the economic, social, cultural, educational, and health fields, and assisting in the realization of intelligent lifeform rights and fundamental freedoms for all without distinction as to culture, sex, language, or religion;
The further responsibilities, functions, and powers of the supreme assembly with respect to matters mentioned in Paragraph 1(b) above are set forth in Chapters IX and X;
Article 14
Subject to the provisions of Article 12, the Supreme Assembly may recommend measures for the peaceful adjustment of any situation, regardless of origin, which it deems likely to impair the general welfare or friendly relations among the planets, including situations resulting from violations of the provisions of the present Charter setting forth the purposes and principles of the United Federation of Planets;
Article 15
The Supreme Assembly shall receive and consider regular and special reports from the Federation Council; which reports shall include an account of the measures that the Federation Council has decided upon or taken to maintain interplanetary peace and security;
The Supreme Assembly shall receive and consider reports from the other agencies of the united Federation on agreed upon regular periods or reporting;
Article 16
The Supreme Assembly shall perform such functions of intergalactic trusteeship as are assigned to it under Chapters XII and XIII, including the approval of the trusteeship agreements for areas which are not designated as strategic;
Article 17
The Supreme Assembly shall consider and approve the budget of the United Federation of Planets;
The expenses of the United Federation of Planets shall be borne by the members as apportioned by the Supreme Assembly;
The Supreme Assembly shall consider and approve any financial and budgetary agreements with specialized agencies referred to in Article 57 and shall examine the administrative budgets of such specialized agencies with a view to making recommendations to the agencies concerned;
All budgets of, and expenses of the United Federation shall be made and paid in the common interplanetary credit. The common interplanetary credit shall be the official medium of exchange within the United Federation treaty exploration territory;
Voting
Article 18
Each member of the Supreme Assembly shall have one (1) vote;
Decisions of the Supreme Assembly on important decisions shall be made on a two-thirds (2/3) majority vote of the members present and voting. These questions shall include: recommendations with respect to the maintenance of interplanetary peace and security; the election of non-permanent members to the Federation Council; the election of members of the trusteeship council in accordance with Paragraph 1(c) of Article 86; the admission of new members to the Federation; the suspension of the rights and privileges of membership; the expulsion of members; questions relating to the operation of the trusteeship system; and budgetary questions;
Decisions on other questions, including the determination of additional categories of questions to be decided by a two-thirds (2/3) majority, shall be made by a majority vote of the members present and voting;
Article 19
A member of the United Federation which is in arrears in the payment of its financial obligations to the Federation shall have no vote in the Supreme Assembly if the amount it is in arrears equals or exceeds the amount of the contributions due from it for the preceding two accounting periods. The Supreme Assembly may, nevertheless, permit such a member to vote if it is satisfied that the failure to pay is due to conditions beyond the control of the member.
Procedure
Article 20
The Supreme Assembly shall meet in regular periodic sessions and in such special sessions as occasion may require. Special sessions shall be convoked by the President at the request of the Federation Council or of a majority of the members of the United Federation.
Article 21
The Supreme Assembly shall adopt its own rules of procedure. It shall elect its president for each session.
Article 22
The Supreme Assembly may establish such subsidiary agencies as it deems necessary for the performance of its functions.