There's noting in the CONstitution that gives the Feral government the authority to control bank accounts. Bank account privacy would be protected under the 4th amendment of the Bill of Rights.
The right of the people to be secure in their persons, houses, papers, and effects,[a] against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.