I don't wear hats much. It is too hard to keep them in place on top of my wig. I have one nice sun hat that fits over my wig that I'll sometimes wear.
But I do wear hats any time I am wigless. If I'm out in the yard, I most often wear a ball cap. For hiking, I wear a rain/sun hat with a brim all the way around. In winter, I wear a tuque. (I think that's what you call a "bobble hat".) Of course, if I am outside wearing a hat, it has to stay on. One time, we made a spur of the moment decision to have a restaurant meal. I had to keep my tuque on through the meal. Fortunately, women can get away with that.