Coal Energy Bridge Act of 2010 - Amends the Internal Revenue Code to: (1) allow seven-year amortization of mechanical or electronic systems that are installed on a coal-fired electric generation unit and that reduce carbon dioxide emissions; (2) allow a new 30% tax credit for investment in carbon dioxide capture, transport, and storage property which is part of a qualified coal-fired electric generation unit; (3) expand the tax credit for carbon dioxide sequestration to allow for uses other than as tertiary injectants; and (4) allow a tax credit for investment in clean energy coal bonds.