I can go a long while before needing to wet, so it's not that often that I need to change in a public place, even after several lengthy stints of 24/7. I was traveling recently, and while I can hold it a good while, that was more than was practical. I had to change several times in public restrooms. Most were busy. I had some twinges of embarrassment but I realized my needs were every bit as legitimate as anyone else in there. It might be my weird choice but the fact remained that I needed a change. I took care of it with minimal fuss and was on my way before long. The biggest deal was in my own mind.
Good on you for apparently coming to the same conclusion.