Bipartisan Commission on Medicaid Act of 2005 - Establishes the Bipartisan Commission on Medicaid to review: (1) each of Medicaid's major functional responsibilities; (2) issues that either threaten or improve the long-term financial condition of Medicaid; (3) Federal and State policies for Medicaid and Medicare enrollment (including enrollment sites), income eligibility, outreach, and documentation; (4) the operation and effectiveness of Medicaid premium assistance programs; and (5) Medicaid payment policies.