I wear cycling specific shorts under regular shorts because I am modest. However, f I go on an extended ride in the summer I will ditch the regular shorts but carry them in my bag so when I dismount for going into a store I can slip them on.
this is also a great way to deal w walking past colleagues at work
cycling shorts fit under anything but I prefer thin lined trishorts by Zoot - got them from Amazon. I was sure to get a large enough size so that they were comfortable. I've got a 38-40 waist so use the XL size. also the Zoot has a regular height waistband as opposed to many other trishorts which have low cut waists.
there's a place I stop that gives cyclists in general a dirty look when they come in to purchase drinks or snacks regardless of what they are wearing. I don't know what their problem is though. It's not just me either, it's to anyone wearing cycling clothes.