Big Oil Bailout Prevention Unlimited Liability Act of 2018 This bill amends the Oil Pollution Act of 1990 to revise requirements governing the liability of parties that are responsible for oil discharges from offshore facilities into navigable waters or adjoining shorelines. Under current law, responsible parties are liable for the total of all removal costs plus $75 million. The bill: (1) removes the cap of $75 million on liability, and (2) makes the responsible parties liable for all covered damages. Covered damages includes damages for: (1) loss of natural resources, property, revenue, or profits; or (2) costs of providing increased public services during or after removal activities, such as fire protection.