Stopping Abortion Bounties Act This bill imposes a 100% tax on amounts received as statutory damages under a state bounty statute. A bounty statute is a statute that authorizes a person to file a civil action and collect damages for assisting another person in exercising the right to have an abortion. The bill also directs the Department of the Treasury to award a grant to any person who pays or incurs amounts under a court order resulting from a suit filed under a bounty statute, including the amount paid or incurred as statutory damages and reasonable attorney's fees.