The critical key is to make sure you are prepared to miss your flight. That way, they lose that ability to intimidate. Also - be unfailingly polite and non-adversarial. If they start to raise their voice/voices, lower yours. This is an incredibly effective technique in controlling an interaction - especially when you are being accosted by an inexperienced and poorly trained TSO.

Next, I would get out a pen and paper, and methodically take as good notes as you possibly can. If you are prevented from doing so, ask for a LEO to be summoned immediately.

At that point, answer any question you wish to answer, and always be completely honest in your response. If you think the question is inappropriate or you do not wish to respond, state as much, decline to answer, and ask for a supervisor AND an LEO to be summoned.

At this point, the BDO will likely back down and allow you to go on your way. If they don't, hold your ground. Continue to avoid escalating the confrontation - politely refuse to answer questions, but ask if you are being detained under what grounds you are being detained, and if you have a lawyer, ask for the opportunity to contact him/her.