After dry cleaning, hang it outside or under cover so the wind and fresh air can remove any lingering dry cleaning smells. This should be done with everything that is dry cleaned.
Then do as these clever forum writers have suggested and make a cover for it. You could sew or tack the 4 corners so it will always be in line, and easy to remove for cleaning. And I'll bet that after some time, maybe years, your tastes will change and this way you can make new covers to match any new bedrooms.