I agree with you... except in what the trust is in. You're saying that the trust is in the authority that produces the bank notes. I do not trust the US government or the Federal Reserve at all, and yet I'd still trust that the USD is a reliable currency simply because other people trust it.

That's why Bitcoin is useful. It has value because people trust that it has value, and when they don't it doesn't. You can buy stuff for bitcoin because people trust that they'll be able to buy things with it.

Underneath it all, we do just have a barter trade system. But we're using an intermediate currency as a globally-recognised IOU. It used to be an IOU for a precious metal (since the precious metals were working as an IOU), but now it's an IOU for any resource, be it working time (employment), games consoles (purchase) or food (purchase) because the little bits of paper are now the currency.

Except we're shifting away from that as well; now it's little numbers.