It's plastic, right? So why not try a Plastic-specific cleaner/polish like Meguiar's Plastx or #10/#17 combo? I've found Plexus to be a good maintenence item (for my plastic rear window), but not a great cleaner.
Plexus is a great product but a very light cleaner, try the Plast-X it has cut thorugh some nasty stuff on headlights, just try on an inconspicous area since I'm unsure of the thickness of those bras and compatibility. But otherwise should be fine:xyxthumbs