Hate being wet - which sports bra actually dries?

Hi:

Despite the sentiment that one is going to be sweaty on race day anyway so who cares about a wet sports bra - that is not me!  I hate thick wet sports bras!  Totally uncomfortable!!

Can someone please share their experience with what would be the fastest drying sports bra - that actually dries.  I read a lot about Moving Comfort.  Is that the only one that dries?

I am a size 34D and thought of just wearing a singlet, but I am not sure it has enough support.  I lost a lot of weight through healthy eating and exercise (went from 340 lbs to 145-150 pounds depending on the day. - wear a pant size of 4/6 - except in tri clothes of course where I am suddenly a Medium/Large).  But my point is - I sort of sag from all the weight loss. 

So back to my question, which sports bra dries faster?  The thought of swimming in a wetsuit and then having a soaked thick sports bra -- eww.

Thanks! :-)

dbw27