Idk about going forward in general besides truly believing that people are fundamentally ‘good’ and there’s almost always nothing to fear… but I do think you’re gonna have to apologise to the lady and explain what happened. It ain’t a crime to be shy, and it would reassure her. Maybe compliment her if you’re feeling brave! Or at least say something like “it’s kinda brave to approach people randomly, I wish I were as comfortable…”, that sounds like a good follow up to the apology.