The most obvious way is to make it a crime to exchange bitcoin for USD, goods, or services. (Doesn't even have to be bitcoin specifically; they can say "blockchain-backed digital resources" or whatever.) Scope it under interstate commerce, in the US; who's going to stop them? Obviously that wouldn't kill BTC overnight, but it would kill any legitimate market. If they're really worked up they can compel financial entities to disclose or block payments to/from known BTC exchanges, or compel telcos to do the same for blockchain mining traffic. They could even ban owning bitcoin; delete your keys or you're committing a felony.
How wouldn't they ban bitcoin, really?
In that scenario I suppose bitcoin's only hope would be that the countries of the world wouldn't coordinate to enforce a global ban. Seems unlikely that they would. But, back to your point, a total US ban might be enough to eventually kill the ecosystem.
Step 2: make use of Bitcoin illegal. You know, "ban" it. It's a plaintext P2P protocol, not exactly magic. If you control the network, you can identify Bitcoin nodes and charge their owners, exactly how law enforcement can enforce laws against other illicit P2P traffic. This would drive any remaining die-hard users to services like Tor.
Step 3: if Bitcoin is somehow still popular enough to be considered a problem, block Tor.
“One has a moral responsibility to disobey unjust laws.” ― Martin Luther King Jr.