The problem with your analogy is that once spent, your bits become worthless. If for instance, I made a song and then you pirated it and then I no longer had it

The problem with your analogy is that once spent, your bits become worthless. If for instance, I made a song and then you pirated it and then I no longer had it on my hard drive any more, then that is what's happening here. Similarly, my password to my bank account is "just bits on a computer", but you could steal that from me, and take all of my [real] money. In that sense, it is theft. Piracy is copying, theft is moving.