You Can't Get Naked in a Triathlon?

In my spare time I've been googling local and localish triathlon's trying to compile my triathlon schedule for the summer.  As I was perusing Athleta's Iron Girl website when I found this in the FAQ Section:

Q.

What do I wear?

A.

Wear something you can COMFORTABLY swim, bike and run in. Practice in your race wear (and get it wet before riding/running in it so you know it doesn’t cause chafes or wedgies while wet). You

can add clothing to your body during transitions but you cannot strip down in the big field and get

naked to change (and there is no changing tent).

I don't know why I assumed 100s (1000s?) of people would just go ahead and get naked together, but i totally did!!   So now I have to start reconsidering all of my race outfit options!  

First I am definitely wearing a wetsuit, I can't stand the cold AT ALL!!  But what to wear underneath? 

I think it's most logical to wear a sports bra because we'll I'll definitely need it later for the run!!  

But what about panties?  Swim bottoms?  Is there some sort of fast drying hybrid panties/shorts thingie that I could wear???  (commence google search NOW)  

Since we can add things, obviously I NEED my bike shorts.  But I'll need another pair to actually run in.  Whatever tank top I decide on can be worn for both bike and run, so that's the one part I'm not actually worried about.  And I'm wearing my sneakers to bike in since I can't actually clip in and out YET.  

So yeah I can't get naked during the triathlon.  What do you wear during the swim?  And do people that don't wear wetsuit wear a one piece bathing suit THE WHOLE TIME?  Does that result in wedgies???