I would buy a cheap tablet or an iPod touch or something, use it only at public wifi spots, only ever use it for this purpose, keep music or whatever on it as a cover, and wipe the device as frequently as possible.
Not foolproof, but reasonably practical.
Thus, you need to be logging on from IP addresses that have no connection to you or your whereabouts. Maybe if you could arrange to VPN into a Russian office that does not keep logs and laughs at FBI subpoenas. Even then, there's the danger they traffic-analyze the data in and out of the VPN server.