Spread the bread on both sides with 2 tablespoons of the butter.
Cook the bread in a large skillet over medium heat until browned, 2 to 3 minutes per side. Remove from the skillet.
Wipe out the skillet and melt the remaining 4 tablespoons of butter over medium-high heat. Add the garlic and cook, stirring, for 1 minute.
Add the wine and bring to a boil.
Add the shrimp, season with ½ teaspoon salt and ¼ teaspoon pepper, and simmer until opaque throughout, 2 to 3 minutes.
Fold in the beans and arugula and cook just until the beans are heated through, 1 to 2 minutes. Serve over the bread.