Truth be told, there's no way to hide yourself with bitcoin from government's surveillance agencies.
Well, this depends on whom you are being targeted by.
There is a huge difference between being swept up in one of the many different mass surveillance programs being run by many different governments, and being targeted specifically as an individual by an FBI investigation or similar. For the vast majority of people, who are not doing anything illegal, it is the lower level mass surveillance and general unwarranted invasion of privacy that you want to avoid. You can absolutely avoid this through using Tor, running your own node, mixing and coinjoining, being careful with your transactions, etc. These mass surveillance programs do not have the time or resources to investigate every person who makes themselves hard to trace. They are not designed to fight crime, prevent terrorism, catch pedophiles, and so on. They are designed for population control, and covering 99% of the population is sufficient to do that.
If, on the other hand, you are already being targeted specifically, then you probably have much bigger things to worry about than the privacy of your bitcoin transactions.
An analogy might be whether it is Facebook or your government who are trying to track your internet activity. If you don't have a Facebook account, never visit Facebook, block all Facebook trackers and ads, make sure your devices have no Facebook apps or software on them, and so on, then you'll do a very good job of keeping Facebook out of your life. But for a government agency pulling data from your ISP, then this is all irrelevant.