Ugh, that's annoying, it would bug me too.
I would get it dry-cleaned myself - maybe speak to the shop and see if they recommend anywhere in particular, and always check for recommendations beforehand.
I'd suggest getting it cleaned after you've had all of your fittings so it's nice and fresh for your wedding, but it might be worth getting it done now, just in case it changes the fit at all - although I don't think it should! Again, ask the bridal shop for their advice. X