[dragonwriter]

> On what basis could a company be banned from accepting it?

If by basis you mean authority, the Commerce Clause is most likely, though I suppose the Coinage Clause might be invoked as well.

If by basis you mean policy motivation, there's an infinite number of possibilities.

> No physical items are exchanged.

Government regulates acts that don't involve an exchange of "physical items", but just electronic data, all the time (pretty much all instance of wire fraud, CFAA violations, among many examples.)

[jsprogrammer]

I mean basis as, what technological basis would disallow the transmission of Bitcoin transactions, but still allow all other digital communications?

[dragonwriter]

Most government prohibitions don't involve technological barriers. (E.g., the prohibition on murder doesn't involve the existence of technological means which obstruct homicidal acts but not other human interaction.)