In my limited understanding of the US system (I am neither a lawyer, nor resident on your continent) I think you can get to meet FBI agents if you are arrested for a federal crime. The more serious the crime, the longer the meeting. If you did something really nasty, such as saying, for purposes of illustration of a political point, that certain government officials needed to be killed, and making barely credible suggestions as to how that might be brought about, then you could end up talking to a great many FBI agents, for many years, at the taxpayer's expense.
Just because a crime is Federal doesn't mean the FBI will be involved; depends on what you did, whether it's known at the time you did it that there were Federal crimes involved, whether the investigation is something that local cops can handle just fine or that need Federal help, whether the Feds are FBI, DEA, BATF, IRS, or other Federal agencies, etc. Sometimes the crime involves an actual victim and a crime scene, and it may be obvious enough from the crime scene or victim complaint that there are Federal crimes involved and enough complexity or inter-state activity that the local cops will bring in Feds. But sometimes the local cops don't need Federal help. Also, sometimes the "crime" doesn't involve a victim - it's private transactions between parties who aren't complaining about it as long as neither party rips off the other party. Sometimes those "crimes" are discovered by prying local cops, sometimes by prying Feds, and sometimes the activity starts off victimless, there's a dispute, and in the absence of the ability to use the legal system to resolve conflict, the parties resort to the pre-Common-Law Anglo-Saxon method of Trial By Combat to resolve the problem, and the cops discover that the participant has become deceased due to issues of Interstate Commerce, or recognize him from The Files, and bring in the FBI for help. And sometimes the criminals are the BATF, and the FBI are brought in to cover up, er, resolve the situation.