Joint Commission on Budget Process Reform Act of 2018 This bill establishes an independent commission known as the Joint Commission on Budget Process Reform to: study procedures on the budget and federal expenditures; conduct public hearings to examine potential budget process reforms; seek recommendations on ways to reform the congressional budget process; draft a bill that amends the Congressional Budget and Impoundment Control Act of 1974; and report to Congress regarding the proposed bill, findings regarding specified federal budget issues, and any other appropriate matters. Congress must consider the commission's bill using specified expedited legislative procedures.