National Infrastructure Development Bank Act of 2019 This bill establishes the National Infrastructure Development Bank as a government corporation to finance energy, environmental (e.g., drinking water or waste facilities), telecommunications, and transportation infrastructure projects. The National Infrastructure Development Bank Board, established by this bill, must oversee the projects. The board may make loans and loan guarantees to assist in financing infrastructure projects. In addition, the board must establish an American Infrastructure Bond program. Under the program, the board may subsidize interest payments by the issuers of state or local bonds. The bill establishes the National Infrastructure Development Bank Trust Fund and appropriates to the fund an amount equal to the tax receipts attributable to interest payable under the bonds. With the approval of the Department of the Treasury, the board may issue public benefit bonds to provide financing to infrastructure projects. The bill exempts bonds issued by the bank, and the interest on or credits with respect to the bonds, from state or local government taxation. Financial assistance for an infrastructure project must be repayable from dedicated revenue sources that also secure the infrastructure project obligations. The assistance may not exceed 50% of reasonably anticipated project costs.