Big Oil Bailout Prevention Trust Fund Act of 2020 This bill eliminates (1) the $1 billion per incident limitation on expenditures from the Oil Spill Liability Trust Fund for cleanup of oil spills, (2) the $500 million per incident limitation on expenditures from the trust fund for natural resource damage assessments and claims in connection with oil spills, and (3) the limitation on the borrowing authority of the trust fund. The bill also directs the President to promulgate regulations to allow advance payments from the Oil Spill Liability Trust Fund to states and localities to prepare for and mitigate substantial threats from the discharge of oil.