The Fed can't because they only regulate the banking system. Bitcoin obviously operates outside of it.

The Treasury Department -- which Yellen is about to oversee -- has more relevance. They can bring Bitcoin within the purview of existing MSB regulation. They can mandate strict reporting requirements for Bitcoin businesses so that spending or selling your bitcoins comes with onerous AML/KYC. They can work closely with the IRS to leverage new AML/KYC requirements into a tax enforcement and compliance program.