Heat oil in a skillet over medium heat; cook and stir onion until tender and lightly browned, 10 to 15 minutes.
Preheat oven to 400 degrees F (200 degrees C). Place pizza crust on a baking sheet or pizza stone.
Mix sour cream and horseradish together in a bowl; spread onto pizza crust. Layer potato slices over sour cream; top with 1 cup Swiss cheese. Layer onion, prime rib, mushrooms, and green bell pepper on top; cover with remaining 1 cup Swiss cheese.
Bake in the preheated oven until cheese is melted and crust is lightly browned, about 20 minutes.