How do I decline being a bridesmaid in a non-friend's wedding?

You thank her very much for the great honor she has done you. Whether you like the giver or not, a gift is a gift, a complement is a complement, and an honor is an honor. You tell her that while you very appreciative of the honor she does you, you can't accept. Don't explain, don't apologize, just continue to insist that is it impossible, it doesn't work for you, etc.