Semi-professional...
As I mentioned, MOST clear bras should be treated the same as the finish from a detailing perspective and WILL benefit from polishing and application of polymer-type wax.
If your bra has swirls or haze, these can be removed via a DA polisher (such as a porter cable 7424) and the right combination of pads and polishes. I am going to alter my recommendations from earlier in the thread*** on this though.
Start with Meguiars 205 (
http://www.autogeek.net/meguiars-205-polish-8oz.html) or Menzerna Final Polish (
http://www.autogeek.net/menzerna-final-polish.html) and a 5" white, Lake County CCS pad. If that doesn't work, move to a more aggressive orange CCS pad. And keep your polisher speed down unless more is required!!!
***I don't think Meguiars 105 is necessary, and I think starting with a white pad is a less aggressive approach
People are saying they are getting great results on clear bras with Blackfire Wet Diamond...
http://www.autogeek.net/blackfire-wet-diamond-sealant.html This is an excellent polymer wax (technically a sealant).
You can get all of these products from Detailers Domain, or Autogeek, or wherever. I usually use Autogeek as they have a lot of sales.
NOTE: If you are swirling up your bra, you are probably swirling your paint too. I am guessing this is occuring during washed. There is probably swirling/marring occuring when the car is washed and dried. If you are going through a swirl-o-matic car automatic car wash, you are probably in trouble...