First ever Try-a-tri...

I've just signed up to compete in my first triathlon - a try-a-tri in August.  I've always been a swimmer, so that's a good strength to have I think, I'm not too concerned about the bike, and as the run is only 2.5K I'm pretty comfortable with that also - it's more the changeovers and attire that have me thinking now...  specifically, I need to wear a sports bra for the run - there's no way I can run without one, but I can't exactly just pop on a sports bra in the middle of the race! Do other people swim with their sports bras on under their suits? I guess my real concern is about the supportive qualities my the sports bra after it's been through the swim - anyone have any experience here?