Welcome TJ-Relic
Although I don't commute regularly, I do on occasion bike to a meeting or a appointment where I need to change. Your choice of clothes sounds good. I would change out of the bike shorts and into some underwear though because you can breed bacteria in the shorts, as well as you will probably be more comfortable in underwear.

If I am not going somewhere where I have to be professional, I tend to take a skirt like you and just wear my jersey, and change out of the shorts.

Good luck.