Bipartisan Social Security Commission Act of 2023 This bill establishes a temporary commission within the legislative branch to provide Congress with recommendations and proposed legislation to ensure the solvency of the Federal Old-Age and Survivors Insurance Trust Fund and the Federal Disability Insurance Trust Fund (commonly referred to as the Social Security trust funds) for at least 75 years. The bill also sets out expedited procedures for the consideration of legislation proposed by the commission. The commission terminates within 60 days of providing its recommendations and proposed legislation.