It's simple - if you want to stay anonymous you have to be represented by someone who won't disclose your identification and can't be traced back to you. Similar to how internet proxies work. The proxy acts as a payment transmitter.

Another option instead of simply converting to cash for everything, bitcoins can be spent when making purchases.  If the places you would consider spending your coins at don't currently accept bitcoin, each reminder the merchant receives about bitcoin will help make the day where they do accept bitcoins come sooner.

Anything else than real life meeting has the problem of being asymmetric. That means someone has to provide trust.