mik5,
For example, if you are at work and you need to say asher yatzar or a bracha on thunder/ lightning, how would you do it? Would you cover your mouth with your hand? Would you pick up the telephone and pretend that you are talking on the phone?
There is a middle ground between the two extremes of acting embarrassed to do a mitzva and doing the mitzva in a way that is disruptive to the environment you are in. Asher yatzar is, for me, the “toughest” to do in public, but I will pause outside of the bathroom and say it quietly. If someone looks at me quizzically, I will politely smile and hold up my hands. Most people are smart enough to put two and two together – the kippa and tzitzis, doing something unfamiliar, he must be doing a “Jewish thing”). As for bircas hamazon, I agree with iacisrmma – it is extremely helpful to look in a bentcher while bentching. This lets passers by know that you are praying. Have you never put on tefillin in public?