The Constitution is the law. It contains the most serious offenses for those committing treason.
As the Constitution is the law, then it is clear that the Bill of Rights is not suspended for charges of treason, or any other charge.
The Founders were particularly suspicious of the charge of treason due to it being abused by the King of England. Thus they specified the definition as strictly as possible and did not include any provision for the suspension of rights for those thus charged.