Shoppers with this card will receive a 20% discount on their purchase.
Bring this card and get 20% off your purchase.
一つ目の例文のほうが丁寧なので質問者さまの日本語に近いと思います。
Shoppers with this card will receive a 20% discount on their next purchase.
(このカードを持ってお買い物される方は、次回20%割引いたします)
Bring this card and get 20% off your purchase.
(このカードを持参すれば20%OFF)