If you want to mask your identity wouldn't you be better off buying Visa gift cards with cash at a major store and then using them to purchase services online?
Even better to have someone else buy the gift cards and then hand them off to you in a dark alley. Bonus points if you're both wearing trench coats and fedoras.
It is harder than that though. Monero has an issue in that everyone is only doing ringsize=3 transactions, providing little anonymity. If you buy from an exchange then turn around and sell it back, even with different amounts, you will be on a shortlist of suspects.
To do Monero properly you need to wait a while (at least hours, better days) while churning to other addresses, being sure to keep your ringsize and fees looking like everyone else's. Hopefully they will raise the ringsize minimum to 10 in the upcoming hardfork - that will go some way towards fixing the problem.
For now, I bet there will be cases of people happily bouncing to Monero via Shapeshift and getting busted.
I could argue the merits of the ringsize but it would be moot because it's being bumped to 10 in September. So I will just leave this here as a note that the argument that a ringsize of 3 is not very anonymous will be moot in September for future readers.
Even with ringsize 10, it does not help if someone does BTC->XMR->BTC with the same exchange (or an exchange that shares records) without adding some XMR->XMR churn steps inbetween.
My future freedom depends on me getting this right, so I am a bit sensitive on this topic. It took me a while to cut through the fluff and figure out how to churn enough to make it safe. Fortunately I also used multiple Bitcoin mixers on both sides and didn't originally get our Bitcoin investment in a way that's directly linked to any of our identities.
It is somewhat irresponsible of Monero's marketing to make such grandiose privacy claims at the moment. I say this as someone that loves Monero and thinks their team is fantastic, and I'd bet Monero will be the privacy currency winner if it isn't already.
Or using a coin designed to be anonymous and private, like.. Monero. You would still probably be on camera buying a Visa gift card in a retail store. With timestamp.
You don't have to trade for dollars. You can use one or more intermediaries such as gift cards and high resale value goods, just like using proxies to distance yourself. The more hops, the harder it is to connect.
And how do you know that that the Bitcoin mixer you decided to use is not actually operated by the FBI and that they are actually keeping a private log tying bitcoins in with bitcoins out?
It does if you've connected it to a bank account, but if you didn't do that, or you used funds that originated from a bank account to get access to a wallet which wasn't connected to you directly, you could make it a rather difficult trail to follow with certainty